Physics Notes for NEET Chapter 26 PDF

1445 60 Atomic and Nuclear Physics Chapter E3 26 Atomic and Nuclear Physics ID Thomson's Atomic Model J.J. Thomson gave the first idea regarding structure of U atom. According to this model. (1) An atom is a solid sphere in which entire and positive charge and it's mass is uniformly distributed and...

1445 60 Atomic and Nuclear Physics Chapter E3 26 Atomic and Nuclear Physics ID Thomson's Atomic Model J.J. Thomson gave the first idea regarding structure of U atom. According to this model. (1) An atom is a solid sphere in which entire and positive charge and it's mass is uniformly distributed and in which watermelon. D YG negative charge (i.e. electron) are embedded like seeds in Positively charged – – – – – – sphere Electron U Fig. 26.1 (1) Most of the -particles pass through the foil straight away undeflected. (2) Some of them are deflected through small angles. (3) A few -particles (1 in 1000) are deflected through the angle more than 90o. ST (2) This model explained successfully the phenomenon of thermionic emission, photoelectric emission and ionization. (3) The model fail to explain the scattering of - particles and it cannot explain the origin of spectral lines observed in the (4) A few  -particles (very few) returned back i.e. deflected by 180o. (5) Number of scattered particles : N  N spectrum of hydrogen and other atoms. -Scattering Experiment 'Geiger and Marsden (students of Rutherford) studied the scattering of -particles by gold foil on the advice of Rutherford and made the following observations.  r0 Nucleus -particle N(180°)  Fig. 26.3 1 sin ( / 2) 4 1446 Atomic and Nuclear Physics (6) If t is the thickness of the foil and N is the number of (1) Most of the mass (at least 99.95%) and all of the charge particles scattered in a particular direction (i.e.  = constant), it was observed that of an atom concentrated in a very small region is called atomic N t N  constant  1  1 N 2 t2 t nucleus. (7) Distance of closest approach (Nuclear dimension) : (2) Nucleus is positively charged and it's size is of the order particle approach, is called the distance of closest approach (r0). At this distance the entire initial kinetic energy has been converted into potential energy so of the total volume of the atom or less. the velocity vector ( v ) of the -particle from the centre of the nucleus when it is far away from the nucleus is known as impact E3 electrons revolve around the nucleus in the same way as the (8) Impact parameter (b) : The perpendicular distance of planets revolve around the sun. Failure of Rutherford's Model (1) Stability of atom : It could not explain stability of atom ID because according to classical electrodynamics theory an accelerated charged particle should continuously radiate  energy. Thus an electron moving in an circular path around the Nucleus Fig. 26.4 nucleus should also radiate energy and thus move into smaller U b + and smaller orbits of gradually decreasing radius and it should ultimately fall into nucleus. D YG b 10–15 m  1 Fermi. The nucleus occupies only about 10–12 (3) In an atom there is maximum empty space and the 1 1 (Ze ) 2e Ze 2 4 kZe 2 mv 2 .  r0   2 2 4 0 r0 mv  0 mv 2 parameter. It is given as of 60 The minimum distance from the nucleus up to which the - Ze 2 cot( / 2)  b  cot( / 2) 1  4 0  mv 2  2  + e– Instability of atom Fig. 26.6 For large b,  particles will go undeviated and for small b the -particle will suffer large scattering. After U Rutherford's Atomic Model -particles scattering experiment, following ST conclusions were made by Rutherford as regard as atomic structure : (2) According to this model the spectrum of atom must be continuous where as practically it is a line spectrum. (3) It did not explain the distribution of electrons outside the Atom + Nucleus 10–15 m nucleus. Bohr's Atomic Model Bohr proposed a model for hydrogen atom which is also 10–10 m applicable for some lighter atoms in which a single electron Size of the nucleus = 1 Fermi = 10–15 m revolves around a stationary nucleus of positive charge Ze Size of the atom 1 Å = 10–10 m Fig. 26.5 (called hydrogen like atom) Bohr's model is based on the following postulates. Atomic and Nuclear Physics (1) He postulated that an electron in an atom can move i.e. around the nucleus in certain circular stable orbits without emitting radiations. 1 (Ze )e mv  4 0 r 2 r also mvr  (2) Bohr found that the magnitude of the electron's  h  Angular momentum is quantized i.e. L  mv nrn  n    2  2 …. (i) nh 2 ….(ii) From equation (i) and (ii) radius of nth orbit rn  permitted value of the orbit radius. rn = Radius of nth orbit, vn = corresponding speed (3) The radiation of energy occurs only when an electron 4 kZme 2  rn  2 n 2 h 2 0  mZe 2  0.53 n2 Å Z 1 ) 4 0 n2 Z (2) Speed of electron : From the above relations, speed of When electron jumps from higher energy orbit (E2) to lower energy orbit (E1) then difference of energies of these orbits i.e. electron in nth orbit can be calculated as vn  2kZe 2 Ze 2 Z  c  Z   .  2.2  10 6 m / sec nh 2 0 nh  137  n n ID E2 – E1 emits in the form of photon. But if electron goes from E1 to E2 it absorbs the same amount of energy. where (c = speed of light 3  108 m/s) Draw Backs of Bohr's Atomic Model Table 26.1 : Some other quantities for revolution of electron in nth orbit U (1) It is valid only for one electron atoms, e.g. : H, He+, Li+2, Na+1 etc. Quantity Formula D YG Sommerfield these are elliptical. (3) Intensity of spectral lines could not be explained. (4) Nucleus was taken as stationary but it also rotates on its (5) It could not be explained the minute structure in U (6) This does not explain the Zeeman effect (splitting up of ST spectral lines in magnetic field) and Stark effect (splitting up in (1) Angular speed (2) Frequency (3) Time period (4) Angular momentum (5) Dependency on n and Z (2) Orbits were taken as circular but according to spectrum line. (k  E3 jumps from one permitted orbit to another. n2h2 60 where n = 1, 2, 3,..... each value of n corresponds to a own axis. 1447 Corresponding current (6) Magnetic moment n  vn mz e  rn 2 02n 3 h 3 n  Z2 n3 n  n mz 2 e 4  2 4  02n 3 h3 n  Z2 n3 4  02 n 3 h 3 mz 2 e 4 Tn  n3 Z2 Tn  2 4 1 n   h  Ln  mv nrn  n    2  in  e  n  mz 2 e 5 4  02n 3 h 3   Mn  in A  in  rn2 Ln  n in  Z2 n3 Mn  n (where electric field) 0  (7) This does not explain the doublets in the spectrum of magneton) some of the atoms like sodium (5890 Å & 5896 Å) (7) Magnetic field Bohr's Orbits (for Hydrogen and H2-like Atoms) (1) Radius of orbit : For an electron around a stationary nucleus the electrostatics force of attraction provides the Energy L necessary centripetal force eh  Bohr 4m r m, – e Fig. 26.7 v B 0 in 2rn  m 2 z 3 e 7 0 8  03 n 5 h 5 B Z3 n5 1448 Atomic and Nuclear Physics (1) Potential energy : An electron possesses some potential (5) Excitation energy and potential : When energy is given energy because it is found in the field of nucleus potential to an electron from external source, it jumps to higher energy energy of electron in nth orbit of radius rn is given by (Ze ) (e ) kZe 2 U  k.  rn rn The minimum energy required to excite an atom is called (2) Kinetic energy : Electron posses kinetic energy because of it's motion. Closer orbits have greater kinetic energy than mv 2 k. (Ze ) (e )  rn rn2 where R  m. excited state and corresponding potential is called exciting potential. Eexcitation e brought from infinity to form the system. It may also be defined as the energy needed to separate it's constituents to large distances. If an electron and a proton are initially at rest and eV energy will be released. The binding energy of a hydrogen atom is therefore 13.6 eV. U  z2  ch  n2  Z2 Z2   13. 6 eV n2 n2 ID brought from large distances to form a hydrogen atom, 13.6 (7) Energy level diagram : The diagrammatic description of D YG   R ch particular defined as the energy released when it's constituents are n 2 h 2 0 kZe 2 also rn . 2rn mze 2  me 4  z 2  me 4 Hence E    2 2 . 2    2 3  8 0 h  n  8  0 ch the (6) Binding energy (B.E.) : Binding energy of a system is kZe 2 | U |  2rn 2 energy and kinetic energy i.e. E = K + U E of EExcitation  EFinal  EInitial and VExcitation  (3) Total energy : Total energy (E) is the sum of potential  energy E3  Kinetic energy K  excitation 60 outer ones. As we know level. This phenomenon is called excitation. 4 me = Rydberg's constant = 1.09  107 per 8  02 ch3 the energy of the electron in different orbits around the nucleus is called energy level diagram. Table 26.2 : Energy level diagram of hydrogen/hydrogen like atom (4) Ionisation energy and potential : The energy required to ionise an atom is called ionisation energy. It is the energy U required to make the electron jump from the present orbit to the infinite orbit. n= Infinite Infinite 0 eV n=4 Fourth Third – 0.85 eV n=3 Third Second – 1.51 eV n=2 Secon First – 3.4 eV d n=1 First Ground – 13.6 eV Principle Orbit Excited Energy for For H2-atom in the ground state quantum state H2 – atom ST  Z2  13.6 Z 2 eV Hence Eionisation  E  En  0    13.6 2    n  n2  E ionisation   13.6(1) 2 n2 number  13.6 eV Transition of Electron The potential through which an electron need to be When an electron makes transition from higher energy level accelerated so that it acquires energy equal to the ionisation having energy E2(n2) to a lower energy level having energy E1 energy is called ionisation potential. Vionisation  Eionisation e (n1) then a photon of frequency  is emitted Atomic and Nuclear Physics 1449 Hydrogen Spectrum and Spectral Series E2 E2 – E1 = h E1 When hydrogen atom is excited, it returns to its normal unexcited (or ground state) state by emitting the energy it had Fig. 26.8 absorbed earlier. This energy is given out by the atom in the form of radiations of different wavelengths as the electron jumps (1) Energy of emitted radiation down from a higher to a lower orbit. Transition from different     orbits cause different wavelengths, these constitute spectral series which are characteristic of the atom emitting them. When 60 n 22  Rch Z 2    n12   1 1   13.6 Z 2  2  2  n n 2   1 observed through a spectroscope, these radiations are imaged as sharp and straight vertical lines of a single colour. Photon of (2) Frequency of emitted radiation E  h    E E 2  E1   Rc Z 2 h h  1 1    2 2 n   1 n2  + E3 E  E 2  E1   Rc h Z 2 + + wavelength  Spectrum Fig. 26.9 : Emission spectra ID (3) Wave number/wavelength Wave number is the number of waves in unit length 1    c   1 1  13.6 Z 2  RZ 2  2  2      hc  n1 n 2  1  1 1     n2 n2  2   1 The spectral lines arising from the transition of electron forms a spectra series. U   (1) Mainly there are five series and each series is named higher energy orbit to lower energy orbit it emits raidations with after it's discover as Lymen series, Balmer series, Paschen various spectral lines. series, Bracket series and Pfund series. D YG (4) Number of spectral lines : If an electron jumps from If electron falls from orbit n2 to n1 then the number of spectral lines emitted is given by NE  (n 2  n1  1)(n 2  n1 ) 2 U If electron falls from nth orbit to ground state ( i.e. n2 = n and n1 = 1) then number of n (n  1) 2 radiations emitted from hydrogen atom is given by  1 n 2n 2 n12 1   R  2  2     2 1 22  2  (n2  n1 )R  n 2   n1  1  n1  n22  1 inner orbit (electron falls in this orbit) (5) Recoiling of an atom : Due to the transition of electron, photon is emitted and the atom is recoiled Recoil momentum of atom = momentum of photon  h   1 1   hRZ 2  2  2  n n 2   1 Also recoil energy of atom  mass of recoil atom) p2 h2  2m 2m 2  R   where n2 = outer orbit (electron jumps from this orbit), n1 = ST NE  spectral lines emitted (2) According to the Bohr's theory the wavelength of the (where m = Fig. 26.10 1450 Atomic and Nuclear Physics Quantum numbers may be defined as a set of four number with the help of which we can get complete information about all the electrons in an atom. It tells us the address of the electron (3) First line of the series is called first member, for this line wavelength is maximum (max) is present. The average distance of the electron from the (4) Last line of the series is called series limit, for this line wavelength is minimum (min) max (n  1)2  min (2n  1) The principal quantum number takes whole number values, n1 = 1 2.Balmer n2 = 3, 4, 5 … series n1 = 2 3. n2 = 4, 5, 6 … Paschen n1 = 3 series n2 = 5, 6, 7 …  series n1 = 4 n2 = 6, 7, 8 …  ST series λ ma x λ min Region n1 = 5 Ultraviole 1 R 4 3 36 5R 4 R 9 5 Visible 144 7R 9 R 16 7 Infrared t region region region The orbital angular momentum of the electron is given as L  l(l  1) h 2 (for a particular value of n). For a given value of n the possible values of l are l = 0, 1, 2, ….. upto (n – 1) (3) Magnetic quantum number (ml) : An electron due to it's angular motion around the nucleus generates an electric field. This electric field is expected to produce a magnetic field. Under 400 9R 16 R 25 9 Infrared region the influence of external magnetic field, the electrons of a 900 11 R 25 R 36 11 Infrared subshell can orient themselves in certain preferred regions of region space around the nucleus called orbitals. Quantum Numbers An atom contains large number of shells and subshells. These are distinguished from one another on the basis of their size, shape and orientation (direction) in space. The parameters are expressed in terms of different numbers called quantum number. denoted as 1, 2, 3, 4 … or s, p, d, f … This tells the shape of the subshells. 4 3R U 4. Bracket 5. Pfund ID min U max the main shell. These subsidiary orbits within a shell will be D YG n2 = 2, 3, 4 … n = 1, 2, 3, 4,…..  number (l) : This represents the number of subshells present in series series (in H-atom) (2) Orbital quantum number (l) or azimuthal quantum Table 26.3 : Different spectral series 1. Lymen 1 and rn  n 2 n2 E3 n2 R (5) The ratio of first member and series limit can be Transition nucleus and the energy of the electron depends on it. En  For minimum wavelength n2  , n1  n So min  Spectral 60 determines the main energy level or shell in which the electron n 2 (n  1)2  (2n  1)R calculated as of that orbital. (1) Principal Quantum number (n) : This quantum number For maximum wavelength if n1 = n then n2 = n + 1 So max i.e. location, energy, the type of orbital occupied and orientation The magnetic quantum number determines the number of preferred orientations of the electron present in a subshell. The angular momentum quantum number m can assume all integral value between – l to +l including zero. Thus ml can be – 1, 0, + 1 for l = 1. Total values of ml associated with a particular value of l is given by (2l + 1). Atomic and Nuclear Physics (4) Spin (magnetic) quantum number (ms) : An electron in atom not only revolves around the nucleus but also spins about 1451 (2) Aufbau principle : Electrons enter the orbitals of lowest energy first. its own axis. Since an electron can spin either in clockwise As a general rule, a new electron enters an empty orbital direction or in anticlockwise direction. Therefore for any for which (n + l ) is minimum. In case the value (n  l) is equal particular value of magnetic quantum number, spin quantum for two orbitals, the one with lower value of n is filled first. number can have two values, i.e. m s  (Spin up) or order (memorize) 1 (Spin down) 2 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, This quantum number helps to explain the magnetic properties of the substance. ml Spectroscopic E3 l 5f, 6d, 7p, …… (3) Hund's Rule : When electrons are added to a subshell Table 26.4 : Quantum states of the hydrogen atom n Thus the electrons are filled in subshells in the following 60 ms   1 2 where more than one orbital of the same energy is available, their spins remain parallel. They occupy different orbitals until Shell each one of them has at least one electron. Pairing starts only 0 1s 2 0 0 2s 2 1 – 1, 0, 1 2p 3 0 0 3s 3 1 – 1, 0, 1 3p 3 2 – 2, – 1, 0, 1, 2 3d 4 0 0 4s K when all orbitals are filled up. Pairing takes place only after filling 3, 5 and 7 electrons in L p, d and f orbitals, respectively. Nucleus U 0 (1) Rutherford's -scattering experiment established that M D YG 1 ID notation the mass of atom is concentrated with small positively charged region at the centre which is called 'nucleus'. N e– Electronic Configurations of Atoms The distribution of electrons in different orbitals of an atom U is called the electronic configuration of the atom. The filling of e– e– electrons in orbitals is governed by the following rules. ST (1) Pauli's exclusion principle : "It states that no two Fig. 26.11 electrons in an atom can have all the four quantum number (n, l, ml and ms) the same." It means each quantum state of an electron must have a (2) The stability or instability of a particular nucleus is different set of quantum numbers n, l, ml and ms. This principle determined by the competition between the attractive nuclear sets an upper limit on the number of electrons that can occupy a force among the protons and neutrons and the repulsive shell. electrical interactions among the protons. Unstable nuclei N max in one shell = 2n2; Thus Nmax in K, L, M, N …. shells are 2, 8, 18, 32, decay, transforming themselves spontaneously into other structure by a variety of decay processes. 1452 Atomic and Nuclear Physics (3) We could not survive without the 3.90  1026 watt output of one near by fusion reactor, our sun. this, the energy of moving neutron decreases while that of the molecules of the moderator increases. After sometime they both (4) Nuclei are made up of proton and neutron. The number attains same energy. The neutrons are then in thermal of protons in a nucleus (called the atomic number or proton equilibrium with the molecules of the moderator and are called number) is represented by the symbol Z. The number of thermal neutrons. neutrons (neutron number) is represented by N. The total Energy of thermal neutron is about 0.025 eV and speed is number of neutrons and protons in a nucleus is called it's mass (5) Neutrons and proton, when described collectively are Types of Nuclei called nucleons. A single nuclear species having specific values of both Z and N is called a nuclide. The nuclei have been classified on the basis of the number of protons (atomic number) or the total number of nucleons X ; where X denotes A Z E3 (6) Nuclides are represented as 60 about 2.2 km/s. number A so A = Z + N. (mass number) as follows the chemical symbol of the element. (1) Isotopes : The atoms of element having same atomic Neutron ID number but different mass number are called isotopes. All Neutron is a fundamental particle which is essential constituent of all nuclei except that of hydrogen atom. It was isotopes have the same chemical properties. The isotopes of some elements are the following discovered by Chadwick. A free neutron outside the nucleus is 1H 17 0n 1H  1 Proton   0 1 Electron  Antinutrino D YG 1 1 , 1H 2, 1H 3 U unstable and decays into proton and electron. Cl 35 , 17 Cl 37 92 U 235 8O , 92 U 16 , 8 O 17 , 8 O 18 2 He 3 , 2 He 4 238 (2) Isobars : The nuclei which have the same mass number (1) The charge of neutron : It is neutral (A) but different atomic number (Z) are called isobars. Isobars (2) The mass of neutron : 1.6750  10–27 kg occupy different positions in periodic table so all isobars have (3) It's spin angular momentum : 1  h   J -s 2  2  (4) It's magnetic moment : 9.57  10–27 J/Tesla U (5) It's half life : 12 minutes ST (6) Penetration power : High (7) Types : Neutrons are of two types slow neutron and fast neutron, both are fully capable of penetrating a nucleus and causing artificial disintegration. Thermal Neutrons different chemical properties. Some of the examples of isobars are 1H 3 and 2 He 3 , 6C 14 and 7 N 14 , 8 O 17 and 9F 17 (3) Isotones : The nuclei having equal number of neutrons are called isotones. For them both the atomic number (Z) and mass number (A) are different, but the value of (A – Z) is same. Some examples are 4 Be 9 and 5 B10 , 6 C13 and 7 N 14 , 8 O18 and 9 F19 3 Li 7 and 4 Be 8 , 1 H 3 and 2 He 4 Fast neutrons can be converted into slow neutrons by (4) Mirror nuclei : Nuclei having the same mass number A certain materials called moderator's (Paraffin wax, heavy water, but with the proton number (Z) and neutron number (A – Z) graphite) when fast moving neutrons pass through a moderator, interchanged (or whose atomic number differ by 1) are called they collide with the molecules of the moderator, as a result of mirror nuclei for example. Atomic and Nuclear Physics 3 7 and 2 He , 3 Li and 4 Be scientist Yukawa the nuclear force between the two nucleons is Size of Nucleus (1) Nuclear radius : Experimental results indicates that the nuclear radius is proportional to A1/3, where A is the mass  R  R 0 A 1 / 3 , where R0 = R  A1 / 3 (2) Nuclear volume : The volume of nucleus is given by called nuclear density. Mass of nucleus mA  Volume of nucleus 4  (R A 1 / 3 )3 0 3 them i.e. n n' 0 Thus exchange of  meson between nucleons keeps the kg) and mA = Mass of nucleus  2.38  10 kg / m 17 and p p' 0 nucleons bound together. It is responsible for the nuclear forces. ID 10–27 3 Dog-Bone analogy The above interactions can be explained with the dog bone analogy according to which we consider the two interacting Nuclear Force D YG Forces that keep the nucleons bound in the nucleus are called nuclear forces. (A) At low speeds, (B) At high speeds, nuclei come electromagnetic repulsion close enough for the strong prevents the collision of nucleons to be two dogs having a common bone clenched in between their teeth very firmly. Each one of these dogs wants to take the bone and hence they cannot be separated easily. They seem to be bound to each other with a strong attractive force (which is the bone) though the dogs themselves are strong enemies. The meson plays the same role of the common bone in between two nucleons. force to bind them together. Fig. 26.12 U nuclei The forces between a pair of neutrons or a pair of protons U 4R 03 n p   are the result of the exchange of neutral meson (o) between where m = Average of mass of a nucleon (= mass of proton   The force between neutron and proton is due to exchange p    n, (3) Nuclear density : Mass per unit volume of a nucleus is 3m  - mesons are of three types – Positive  meson (+), of charged meson between them i.e. 4 4  R 3   R 03 A  V  A 3 3 + mass of neutron = 1.66  the nucleons. negative  meson ( –), neutral  meson (0) 1.2  10–15 m = 1.2 fm. Nuclear density( )  the result of the exchange of particles called mesons between 60 number of nucleus i.e. V 1453 (6) Nuclear forces are exchange forces : According to 7 E3 1H 3 Fig. 26.13 ST (1) Nuclear forces are short range forces. These do not exist at large distances greater than 10–15 m. (2) Nuclear forces are the strongest forces in nature. (3) These are attractive force and causes stability of the nucleus. (4) These forces are charge independent. (5) Nuclear forces are non-central force. Atomic Mass Unit (amu ) (1) In nuclear physics, a convenient unit of mass is the unified atomic mass unit abbreviated u. 1454 Atomic and Nuclear Physics (2) The amu is defined as 1 th mass of a 12 BC 12 called pair production and may be represented by the following at on. equation (3) 1 amu (or 1 u) = 1.6605402  10–27 kg. h (  photon) 0 1 (Positron)  (4) Masses of electron, proton and neutrons :  +1 0 h +Ze -photon Nucleus Mass of electron (me) = 9.1  10–31 kg = 0.0005486 amu, Mass of proton (mp) = 1.6726  10–27 kg = 1.007276 amu  –1 0 60 Mass of neutron (mn) = 1.6750  10–27 kg = 1.00865 amu, Mass of Fig. 26.14 hydrogen atom (me + mp) = 1.6729  10–27 kg = 1.0078 amu large, of the order of MeV. The rest-mass energy of each of positron and electron is (6) According to Einstein, mass and energy are inter convertible. The Einstein's mass energy relationship is given by E  mc 2 amu is equivalent to 931 MeV or 1 amu (or 1 u) = 931 MeV MeV MeV (1 u) c = 931 MeV  1u  931 2 or c 2  931 u c Table 26.5 : Neutral atomic masses for some light nuclides Deuterium (1 H ) 2 Tritium (1 H ) 3 Helium (2 He ) 3 Helium (2 He ) 4 Lithium (3 Li) U 7 Atomic mass (u) D YG 1 Beryllium (4 Be ) 9 1.007825 Compton effect on striking the matter. The converse phenomenon pair-annihilation is also possible. Whenever an electron and a positron come very close to each other, they annihilate each other by combining together and two -photons (energy) are produced. This phenomenon is equation. 3.016029 0 1  (Positron)  0 1  (Electron)  h ( - photon )  h ( - photon ) 4.002603 7.016004 9.012182 14.003074 Oxygen (8 O) 15.994915 ST -photon is less than this, it would cause photo-electric effect or 3.016049 Nitrogen (7 N ) 16 -photon must be at least 2  0.51 = 1.02 MeV. If the energy of called pair annihilation and is represented by the following 12.000000 14 Hence, for pair-production it is essential that the energy of 2.014102 Carbon (6 C ) 12 = 8.2  10–14 J = 0.51 MeV U 2 E0 = m0c2 = (9.1  10–31 kg)  (3.0  108 m/s)2 ID If m = 1 amu, c = 3  108 m/sec then E = 931 MeV i.e. 1 Hydrogen (1 H ) E3 (5) The energy associated with a nuclear process is usually Element and isopore 0 1  (Electron)  Pair Production and Pair-Annihilation When an energetic -ray photon falls on a heavy substance. It is absorbed by some nucleus of the substance and an electron and a positron are produced. This phenomenon is Nuclear Stability Among about 1500 known nuclides, less than 260 are stable. The others are unstable that decay to form other nuclides by emitting , -particles and  - EM waves. (This process is called radioactivity). The stability of nucleus is determined by many factors. Few such factors are given below : (1) Neutron-proton ratio N   Ratio  Z  : The chemical properties of an atom are governed entirely by the number of protons (Z) in the nucleus, the stability of an atom appears to Atomic and Nuclear Physics 1455 depend on both the number of protons and the number of neutron excess in N – Z = 43. There are no stable nuclides with neutrons. Z > 83. (i) For lighter nuclei, the greatest stability is achieved when (2) Even or odd numbers of Z or N : The stability of a the number of protons and neutrons are approximately equal (N nuclide is also determined by the consideration whether it  Z) i.e. contains an even or odd number of protons and neutrons. N 1 Z (i) It is found that an even-even nucleus (even Z and even neutrons than protons. Thus heavy nuclei are neutron rich compared to lighter nuclei (for heavy nuclei, more is the number 60 (ii) Heavy nuclei are stable only when they have more N) is more stable (60% of stable nuclide have even Z and even N). (ii) An even-odd nucleus (even Z and odd N) or odd-even between them. Therefore more neutrons are added to provide nuclide (odd Z and even N) is found to be lesser sable while the the strong attractive forces necessary to keep the nucleus odd-odd nucleus is found to be less stable. E3 of protons in the nucleus, greater is the electrical repulsive force stable.) ID (iii) Only five stable odd-odd nuclides are known : 1H 104 96 75 Ta 180 is determined by value of it's binding energy per nucleon. In U 80 72 general higher the value of binding energy per nucleon, more 64 56 48 40 32 24 16 8 8 D YG Neutron number (N) , 3 Li 6 , 5 Be 10 , 7 N 14 and (3) Binding energy per nucleon : The stability of a nucleus 86 0 2 16 24 32 40 48 56 64 72 80 88 96 stable the nucleus is Mass Defect and Binding Energy (1) Mass defect (m) : It is found that the mass of a nucleus is always less than the sum of masses of it's constituent nucleons in free state. This difference in masses is called mass defect. Hence mass defect U Atomic number (Z) ST Fig. 26.15 (iii) Figure shows a plot of N verses Z for the stable nuclei. For mass number upto about A = 40. For larger value of Z the nuclear force is unable to hold the nucleus together against the electrical repulsion of the protons unless the number of neutrons exceeds the number of protons. At Bi (Z = 83, A = 209), the m = Sum of masses of nucleons – Mass of nucleus      Zm p  ( A  Z)m n  M  Zm p  Zm e  ( A  Z)m z  M ' where mp = Mass of proton, mn = Mass of each neutron, me = Mass of each electron M = Mass of nucleus, Z = Atomic number, A = Mass number, M = Mass of atom as a whole. (2) Packing fraction : Mass defect per nucleon is called packing fraction 1456 Atomic and Nuclear Physics m M  A  A A Packing fraction (f )  where M = Mass of (4) Binding energy per nucleon : The average energy required to release a nucleon from the nucleus is called binding nucleus, A = Mass number energy per nucleon. Packing fraction measures the stability of a nucleus. Binding energy per nucleon Smaller the value of packing fraction, larger is the stability of the (i) Packing fraction may be of positive, negative or zero value. Total binding energy m  931 MeV  Mass number (i.e. total number A Nucleon of nucleons) 60  nucleus. Binding energy per nucleon  Stability of nucleus Binding Energy Curve (ii) At A = 16, f Zero E3 It is the graph between binding energy per nucleon and total number of nucleons (i.e. mass number A) 40 30 20 number ( A) 6.0 Li 4.0 2.0 0 U Fig. 26.16 nucleon (MeV) – 10 – 20 Mass Fe56 8.0 He ID A > 240 Binding energy per 26 10 0 H2 50 56 D YG (3) Binding energy (B.E.) : The neutrons and protons in a 100 150 200 Mass number A Fig. 26.17 stable nucleus are held together by nuclear forces and energy is needed to pull them infinitely apart (or the same energy is released during the formation of the nucleus). This energy is called the binding energy of the nucleus. or U The binding energy of a nucleus may be defined as the energy equivalent to the mass defect of the nucleus. ST If m is mass defect then according to Einstein's mass energy relation Binding energy = m  c2 = [{mpZ + mn(A – Z)} – M] c2 (This binding energy is expressed in joule, because m is measured in kg) If m is measured in amu then binding energy = m amu = [{mpZ + mn(A – Z)} – M] amu = m  931 MeV (1) Some nuclei with mass number A < 20 have large binding energy per nucleon than their neighbour nuclei. For example 2 He 4 , 4 Be 8 , 6 C 12 , 8 O 16 and 10 Ne 20. These nuclei are more stable than their neighbours. (2) The binding energy per nucleon is maximum for nuclei of mass number A = 56 ( 26 Fe 56 ). It's value is 8.8 MeV per nucleon. (3) For nuclei having A > 56, binding energy per nucleon gradually decreases for uranium (A = 238), the value of binding energy per nucleon drops to 7.5 MeV. Nuclear Reactions The process by which the identity of a nucleus is changed when it is bombarded by an energetic particle is called nuclear Atomic and Nuclear Physics reaction. The general expression for the nuclear reaction is as (iii) Conservation of energy : Total energy before the reaction is equal to total energy after the reaction. Term Q is follows. C  a (Incident particle) (Compound nucleus)  added to balance the total energy of the reaction.  Y (Compound nucleus)  (3) Common nuclear reactions : The nuclear reactions  Q b (Product particles) lead to artificial transmutation of nuclei. Rutherford was the (Energy) Here X and a are known as reactants and Y and b are known as products. This reaction is known as (a, b) reaction first to carry out artificial transmutation of nitrogen to oxygen in the year 1919. and can be represented as X(a, b) Y 2 He absorbed or released during nuclear reaction is known as Qvalue of nuclear reaction. = (Mass of reactants – mass of products) amu If Q < 0, The nuclear reaction is known as endothermic. If Q > 0, The nuclear reaction is known as exothermic (The D YG (2) Law of conservation in nuclear reactions (i) Conservation of mass number and charge number : In the following nuclear reaction 2 He  7N 14 8O  1H 1 Before the reaction U Mass number (A) 17 4 +14 = 18 ST (p, n) reaction  1H 1  5 B 11 6 C 12 6 C 11  0 n1 (p, ) reaction  1H 1  3 Li 11 4 Be 8 2 He 4  2 He 4 (p, ) reaction  1H (n, p) reaction  0n 1 1  6 C 12 7 N 13 7 N 13    7 N 14 7 N 15 6 C 14  1 H 1 (, n) reaction    1 H 2 1 H 1  0 n1 Nuclear Fission energy is released in the reaction) 4 given as follows. U (The energy is absorbed in the reaction) It is called (, p) reaction. Some other nuclear reactions are ID Q-value = (Mass of reactants – mass of products)c2 Joules  7 N 14 9 F 18 8 O 17  1 H 1 E3 (1) Q value or energy of nuclear reaction : The energy 4 60 X (Parent nucleus) reaction 1457 Charge number (Z) 2 + 7 = 9 After the (1) The process of splitting of a heavy nucleus into two lighter nuclei of comparable masses (after bombardment with a energetic particle) with liberation of energy is called nuclear fission. (2) The phenomenon of nuclear fission was discovered by scientist Ottohann and F. Strassman and was explained by N. Bohr and J.A. Wheeler on the basis of liquid drop model of 17 + 1 = 18 nucleus. Fission 8+1=9 fragment (ii) Conservation of momentum : Linear momentum/angular momentum of particles before the reaction is equal to the linear/angular momentum of the particles after the reaction. That is p = 0 235 U Fission Neutron s fragmen Fig. 26.18 t Neutron s 1458 Atomic and Nuclear Physics (3) Fission reaction of U235 92 U 235  0 n1 236 92 U (unstable nucleus) (13) Most of energy released appears in the form of kinetic 141 56 Ba  36 Kr 92 energy of fission fragments.  3 0 n1  Q (4) The energy released in U235 fission is about 200 MeV or Energy Slow 0.8 MeV per nucleon. Neutron 92 U 235 92 U235 92 U236 Energy , on an average 2.5 neutrons are 60 (5) By fission of Ba Energy Energy liberated. These neutrons are called fast neutrons and their Kr energy is about 2 MeV (for each). These fast neutrons can Fig. 26.19 escape from the reaction so as to proceed the chain reaction (6) Fission of U235 occurs by slow neutrons only (of energy E3 they are need to slow down. Chain Reaction about 1eV) or even by thermal neutrons (of energy about 0.025 In nuclear fission, three neutrons are produced along with ID eV). the release of large energy. Under favourable conditions, these neutrons can cause further fission of other nuclei, producing energy. This is equivalence to 20,000 tones of TNT explosion. large number of neutrons. Thus a chain of nuclear fissions is U (7) 50 kg of U235 on fission will release  4 × 1015 J of established which continues until the whole of the uranium is explosion power. consumed. D YG The nuclear bomb dropped at Hiroshima had this much (8) The mass of the compound nucleus must be greater 90 37 than the sum of masses of fission products. (9) The Binding energy of compound nucleus must be less A than that of the fission products. U (10) It may be pointed out that it is not necessary that in each fission of uranium, the two fragments 56 Ba and 36 Kr are Fission fragment First generation 94 36 Kr neutron Lost n 0 1 neutron 92 U235 139 56 Ba Fission atoms. fragment ST formed but they may be any stable isotopes of middle weight (11) Same other U 235 fission reactions are 92 U 235  0n 54 Xe 1 140  38 Sr 94 called prompt neutrons. neutrons 90 38 Sr 143 54 Xe Third generation neutrons  20 n (12) The neutrons released during the fission process are Cs generation 1 Many more 144 55 Second 1 0n 57 La 148  35 Br 85  3 0 n 1 Rb Fig. 26.20 1 0n Atomic and Nuclear Physics 1459 In the chain reaction, the number of nuclei undergoing The chain reaction once started will remain steady, fission increases very fast. So, the energy produced takes a accelerate or retard depending upon, a factor called neutron tremendous magnitude very soon. reproduction factor (k). It is defined as follows. Difficulties in Chain Reaction k In chain reaction following difficulties are observed uranium is the isotope U238 (99.3%), the isotope U 235 is very little (0.7%). It is found that U 238 is fissionable with fast If k = 1, the chain reaction will be steady. The size of the fissionable material used is said to be the critical size and it's mass, the critical mass. 60 (1) Absorption of neutrons by U238 : the major part in natural Rate of product ion of neutrons Rate of loss of neutrons If k > 1, the chain reaction accelerates, resulting in an to the large percentage of U 238 , there is more possibility of explosion. The size of the material in this case is super critical. collision of neutrons with U 238. It is found that the neutrons get (Atom bomb) slowed on coliding with U 238 , as a result of it further fission of is not possible (Because they are slow and they are absorbed by U 238). If k < 1, the chain reaction gradually comes to a halt. The ID U 238 E3 neutrons, whereas U 235 is fissionable with slow neutrons. Due This stops the chain reaction. size of the material used us said to be sub-critical. Table 26.6 : Types of chain reaction 235 is separated 92 U U Removal : (i) To sustain chain reaction from the ordinary uranium. Uranium so obtained  92 U 235  is D YG known as enriched uranium, which is fissionable with the fast Controlled chain reaction Controlled by artificial method Uncontrolled chain reaction No control over this type of nuclear reaction and slow neutrons and hence chain reaction can be sustained. All neurons are absorbed except More than one neutron takes one part into reaction It's rate is slow Fast rate Reproduction factor k = 1 Reproduction factor k > 1 Energy liberated in this type of A large amount of energy is Which reduce the speed of neutron rapidly graphite and heavy reaction is always less than liberated water are the example of moderators. explosive energy reaction Chain reaction is the principle of Uncontrolled chain reaction is nuclear reactors the principle of atom bomb. (ii) If neutrons are slowed down by any method to an energy of about 0.3 eV, then the probability of their absorption by U 238 becomes very low, while the probability of their becomes high. This job is done by moderators. U fissioning U 235 ST (2) Critical size : The neutrons emitted during fission are very fast and they travel a large distance before being slowed down. If the size of the fissionable material is small, the neutrons emitted will escape the fissionable material before they are slowed down. Hence chain reaction cannot be sustained. Removal : The size of the fissionable material should be large than a critical size. in this type of Nuclear Reactor A nuclear reactor is a device in which nuclear fission can be carried out through a sustained and a controlled chain reaction. It is also called an atomic pile. It is thus a source of controlled energy which is utilised for many useful purposes. Cadmium Coolant rods Core Coolant out Turbine Concret To electric e wall generator 1460 Atomic and Nuclear Physics persons working around the reactor from the hazardous radiations. (6) Uses of nuclear reactor (i) In electric power generation. (ii) To produce radioactive isotopes for their use in medical 60 science, agriculture and industry. (iii) In manufacturing of Pu239 which is used in atom bomb. (iv) They are used to produce neutron beam of high E3 intensity which is used in the treatment of cancer and nuclear research. Nuclear Fusion (1) In nuclear fusion two or more than two lighter nuclei combine to form a single heavy nucleus. The mass of single used in the reactor is called the fuel of the reactor. Uranium nucleus so formed is less than the sum of the masses of parent isotope (U235) Thorium isotope (Th232) and Plutonium isotopes nuclei. This difference in mass results in the release of (Pu239, Pu240 and Pu241) are the most commonly used fuels in tremendous amount P of energy U ID (1) Fissionable material (Fuel) : The fissionable material D YG the reactor. (2) Moderator : Moderator is used to slow down the fast P 2 P H P n P n  3 e+ moving neutrons. Most commonly used moderators are graphite He nP P P P n 4 n  P P He P n n P P P Fig. 26.22 and heavy water (D2O). (3) Control Material : Control material is used to control the chain reaction and to maintain a stable rate of reaction. This material controls the number of neutrons available for the U fission. For example, cadmium rods are inserted into the core of the reactor because they can absorb the neutrons. The ST neutrons available for fission are controlled by moving the cadmium rods in or out of the core of the reactor. (4) Coolant : Coolant is a cooling material which removes (2) For fusion high pressure ( 106 atm) and high temperature (of the order of 107 K to 108 K) is required and so the reaction is called thermonuclear reaction. (3) Here are three examples of energy-liberating fusion reactions, written in terms of the neutral atoms. Together the reactions make up the process called the proton-proton chain. the heat generated due to fission in the reactor. Commonly used coolants are water, CO2 nitrogen etc. (5) Protective shield : A protective shield in the form a concrete thick wall surrounds the core of the reactor to save the 1 1H  11 H 12 H      e 2 1H  11 H 32 He   3 2 He  32 He 42 He  11 H  11 H 4 1 H 1 2 He 4  2    2  26.73 MeV Atomic and Nuclear Physics (4) The proton-proton chain takes place in the interior of the sun and other stars. Each gram of the suns mass contains 1461 (1) Radioactivity was discovered by Henery Becquerel in uranium salt in the year 1896. about 4.5  1023 protons. If all of these protons were fused into (2) After the discovery of radioactivity in uranium, Piere helium, the energy released would be about 130,000 kWh. If the Curie and Madame Curie discovered a new radioactive element sun were to continue to radiate at its present rate, it would take called radium (which is 106 times more radioactive than about 75  10 9 years to exhaust its supply of protons. uranium) (6) Plasma : The temperature of the order of 108 K required for thermonuclear reactions leads to the complete ionisation of the atom of light elements. The combination of base nuclei and 60 fusion is much larger than in fission. (3) Some examples of radio active substances are : Uranium, Radium, Thorium, Polonium, Neptunium etc. (4) Radioactivity of a sample cannot be controlled by any physical (pressure, temperature, electric or magnetic field) or chemical changes. E3 (5) For the same mass of the fuel, the energy released in (5) All the elements with atomic number (Z ) > 82 are electron cloud is called plasma. The enormous gravitational field naturally radioactive. of the sun confines the plasma in the interior of the sun. (6) The conversion of lighter elements into radioactive ID The main problem to carryout nuclear fusion in the laboratory is to contain the plasma at a temperature of 108K. No solid container can tolerate this much temperature. If this elements by the bombardment of fast moving particles is called artificial or induced radioactivity. (7) Radioactivity is a nuclear event and not atomic. Hence U problem of containing plasma is solved, then the large quantity electronic configuration of atom don't have any relationship with exhaustible source of energy. radioactivity. D YG of deuterium present in sea water would be able to serve as in- Table 26.7 : Nuclear bomb (Based on uncontrolled Nuclear Radiations According to Rutherford's experiment when a sample of nuclear reactions) Atom bomb Hydrogen bomb fusion process. emission of radiation through a small hole only. When the Based on fission process it Based involves the fission of U235 Mixture of deutron and tritium is radiation enters into the external electric field, they splits into used in it three parts (-rays, -rays and -rays) There is no limit to critical size U In this critical size is important on radioactive substance is put in a lead box and allow the High temperature and pressure temperature and pressure are required ST Explosion is possible at normal Less energy is released compared to hydrogen bomb More energy is released as – – – – –  -rays  -rays  -rays + + + + +   -rays  -rays dangerous than     -rays  field     atom bomb Radioactivity The phenomenon of spontaneous emission of radiatons by heavy elements is called radioactivity. The elements which shows this phenomenon are called radioactive elements. (A) (B) Fig. 26.23   Magnetic  compared to atom bomb so it is more    1462 Atomic and Nuclear Physics (1) -decay : Nearly 90% of the 2500 known nuclides are energetically possible but in which an orbital electron (usually in radioactive ; they are not stable but decay into other nuclides (i) When unstable nuclides decay into different nuclides, they usually emit alpha () or beta () particles. the k-shell) can combine with a proton in the nucleus to form a neutron and a neutrino. The neutron remains in the nucleus and the neutrino is emitted. large to be stable. When a nucleus emits an alpha particle, its N and Z values each decrease by two and A decreases by four. p    n  (3) -decay : The energy of internal motion of a nucleus is 60 (ii) Alpha emission occurs principally with nuclei that are too quantized. A typical nucleus has a set of allowed energy levels, original neutral atom is greater than the sum of the masses of the final neutral atom and the neutral helium- atom. including a ground state (state of lowest energy) and several excited states. Because of the great strength of nuclear E3 (iii) Alpha decay is possible whenever the mass of the interactions, excitation energies of nuclei are typically of the (2) -decay : There are different simple type of -decay  (viii) There are a few nuclides for which   emission is not   ,  and electron capture. order of the order of 1 MeV, compared with a few eV for atomic energy levels. In ordinary physical and chemical transformations  the nucleus always remains in its ground state. When a nucleus   involves transformation of a neutron into a proton, an is placed in an excited state, either by bombardment with high- electron and a third particle called an antineutrino ( ). energy particles or by a radioactive transformation, it can decay decay usually occurs with nuclides for which the to the ground state by emission of one or more photons called U (ii)   ID (i) A beta minus particle ( ) is an electron. Emission of N  neutron to proton ratio  ratio is too large for stability. Z   gamma rays or gamma-ray photons, with typical energies of 10 D YG (iii) In   decay, N decreases by one, Z increases by one and A doesn't change. (iv)   decay can occur whenever the neutral atomic mass of the original atom is larger than that of the final atom. (v) Nuclides for which N/Z is too small for stability can emit a positron, the electron's antiparticle, which is identical to the U electron but with positive charge. The basic process called beta plus   decay All the known conservation laws are obeyed in -decay. The intensity of -decay after passing through x thickness of a material is given by I  I0 e  x ( = absorption co-efficient) Radioactive Disintegration (1) Law of radioactive disintegration : According to Rutherford and Soddy law for radioactive decay is as follows. "At any instant the rate of decay of radioactive atoms is ( = neutrino) ST p n     keV to 5 MeV. This process is called gamma () decay. proportional to the number of atoms present at that instant" i.e. (vi)   decay can occur whenever the neutral atomic mass of the original atom is at least two electron masses larger than that of the final atom (vii) The mass of  and  is zero. The spin of both is units of dN dN N   N. It can be proved that N = N0e–t dt dt In terms of mass M = M0e– t 1 in 2 h. The charge on both is zero. The spin of neutrino is 2 antiparallel to it's momentum while that of antineutrino is parallel to it's momentum.  where N = Number of atoms remains undecayed after time t, N0 = Number of atoms present initially (i.e. at t = 0), M = Mass of radioactive nuclei at time t, M0 = Mass of radioactive nuclei at time t = 0, N0 – N = Number of disintegrated nucleus in time t Atomic and Nuclear Physics 1463 dN = rate of decay,  = Decay constant or disintegration dt constant or radioactivity constant or Rutherford Soddy's constant or the probability of decay per unit time of a nucleus. Table 26.8 : Properties of ,  and -rays 1. Identity - particles  - particles Helium nucleus or doubly  - rays Fast moving electron (  0 or  – ) Photons (E.M. waves) 60 Features ionised helium atom (2He 4) 2. Charge + 2e –e 3. Mass 4 mp ( mp = mass of proton 4 mp me 4. Speed  107 m/s 1% to 99% of speed of light Speed of light 5. Range of kinetic energy 4 MeV to 9 MeV All possible values between a Between a minimum value to minimum certain value to 1.2 MeV 2.23 MeV 100 10,000 (100 times of ) (100 times of  upto 30 cm of Zero E3 Massless 6. Penetration power (, , ) 1 10,000 D YG 7. Ionisation power ( >  > ) U (Stopped by a paper) ID = 1.87  10–27 iron (or Pb) sheet 100 1 8. Effect of electric or magnetic field Deflected Deflected Not deflected 9. Energy spectrum Line and discrete Continuous Line and discrete 10. Mutual interaction with matter Produces heat Produces heat Produces, photo-electric effect, ST U 11. Equation of decay Z  decay  X A  Z 2 Y A 4  2 He 4  X A   Z 'Y A ' n Z  nα  count rate) of the substance (or the number of atoms of any A dN  N  N 0 e t  A 0 e t dt effect, pair production Z X A Z 1 Y A  1 e 0   ZX A Z X A ZXa  n  Z ' X A  n β  (2 n α  Z  Z' ) A  A' 4 (2) Activity : It is defined as the rate of disintegration (or material decaying per second) i.e. Compton where A0 = Activity of t = 0, A = Activity after time t Units of activity (Radioactivity) It's units are Becqueral (Bq), Curie (Ci) and Rutherford (Rd) 1 Becquerel = 1 disintegration/sec, 1464 Atomic and Nuclear Physics 1 Rutherford = 106 dis/sec, 1 Curie = 3.7  1011 dis/sec (3) Half life (T1/2) : Time interval in which the mass of a radioactive substance or the N number of it's atom reduces to curve is known as mean life (). N0 half of it's initial value is called N i.e. if N  0 2 Half life = T ln N0/2 N0/4 0 1 2T 3T t Fig. 26.24 (iii) From N  N 0 e t , if t  Fraction of atoms active atoms (N/N0) decayed (N0 – N) /N0 probability of survival probability of decay 1 (100%) 0 (50%) 1 2 1 4 t = 3(T1/2) 1 8 t = 10 (T1/2) 1   2 10 (50%) t = n (N1/2) 1   2 n (25%) 3 4 (75%) (12.5%) 7 8 (87.5%)  99.9%   1 n  1       2   U  0.1 % (4) Mean (or average) life () : The time for which a ST radioactive material remains active is defined as mean (average) life of that material. (i) or it is defined as the sum of lives of all atoms divided by the total number of atoms i.e.   1  N  N 0 e 1  N 0    0.37 N 0  37% of N0. e  i.e. mean life is the time interval in which number of 1 times or 0.37 times or 37% e undecayed atoms (N) becomes or U t = 2(T1/2)  of original number of atoms. D YG 1 2 1  ID Table 26.9 : Fraction of active/decayed atom at different time t = T1/2 E3 N0 loge 2 0.693  (T1 / 2 )  T1 / 2   N0e    2 Remaining fraction of Sum of the livesof all the atoms 1   Total number of atoms t Fig. 26.25 Hence from N  N 0 e t t=0 Slope = –  N0 then t  T1 / 2 Time (t) N 60 the half life of the substance. N N 0 (ii) From N  N 0 e t    slope of the line shown t N in the graph i.e. the magnitude of inverse of slope of ln vs t N0 ln It is the time in which number of decayed atoms ( N0 – N) 1  becomes  1   times or 0.63 times or 63% of original number e  of atoms. (iv) From T1 / 2  0.693   1    1. (t1 / 2 )  1.44 (T1 / 2 ) 0.693 i.e. mean life is about 44% more than that of half life. Which gives us  > T(1/2) Radioactive Series (1) If the isotope that results from a radioactive decay is itself radioactive then it will also decay and so on. (2) The sequence of decays is known as radioactive decay series. Most of the radio-nuclides found in nature are members of four radioactive series. These are as follows Table 26.10 : Four radioactive series Mass Series number (Nature) 4n Thorium (natural) 4n + 1 Neptunium Parent Stable end Integer n product Pb 208 52 Bi 209 52 90 Th 232 82 93 Np 237 83 Atomic and Nuclear Physics 1465 (Artificial) 4n + 2 Uranium 4n + 3 U 238 82 Pb 206 51 Ac 227 82 Pb 207 51 92 (Natural) Actinium 89 (Natural) (3) The 4n + 1 series starts from 94 (1) In medicine Pu241 but commonly (i) For testing blood-chromium - 51 (ii) For testing blood circulation - Na - 24 lived member of the series. (iii) For detecting brain tumor- Radio mercury - 203 92 U 235. (iv) For detecting fault in thyroid gland - Radio iodine - 131 Successive Disintegration and Radioactive Equilibrium (v) For cancer - cobalt - 60 E3 (4) The 4n + 3 series actually starts from 60 known as neptunium series because neptunium is the longest (vi) For blood - Gold - 189 Suppose a radioactive element A disintegrates to form (vii) For skin diseases - Phospohorous - 31 (2) In Archaeology another element C; such decays are called successive (i) For determining age of archaeological sample (carbon dating) C 14 disintegration. 1 2 B (ii) For determining age of meteorites - K 40 C Fig. 26.26 (iii) For determining age of earth-Lead isotopes U A ID another radioactive element B which intern disintegrates to still (3) In agriculture D YG (i) For protecting potato crop from earthworm- CO 60 Rate of disintegration of A  dN 1  1 N 1 (which is also dt the rate of formation of B) Rate of disintegration of B  dN 2   2 N 2 dt  Net rate of formation of B = Rate of disintegration of A – Rate of disintegration of B U = 1N1 – 2N2 Equilibrium In radioactive equilibrium, the rate of decay of any (ii) For artificial rains - AgI (iii) As fertilizers - P 32 (4) As tracers - (Tracer) : Very small quantity of radioisotopes present in a mixture is known as tracer (i) Tracer technique is used for studying biochemical reaction in tracer and animals. (5) In industries (i) For detecting leakage in oil or water pipe lines (ii) For determining the age of planets. ST radioactive product is just equal to it's rate of production from the previous member. i.e. 1N1 = 2N2  (T ) N 1   2  2  1/2  2 N 2  1 (T1 / 2 )1 Uses of Radioactive Isotopes  According to Bohr theory the momentum of an e  revolving in second orbit of H2 atom will be h   For an electron in the nth orbit of hydrogen atom in Bohr 1466 Atomic and Nuclear Physics model, circumference of orbit  n ; where  = de-Broglie allowed orbit to inner allowed orbit are of some definite wavelength. energy only. They do not have a continuous graduation of  Rch = Rydberg's energy ~– 2.17  10 18 J ~– 13.6 eV. energy. Therefore the spectrum of the emitted light has only  For hydrogen atom principle quantum number 13. 6. (B.E.) n some definite lines and therefore atomic spectrum is line spectrum.  Just as dots of light of only three colours combine to form  In an H 2 atom when e  almost every conceivable colour on T.V. screen, only about excited state to the ground state it’s kinetic energy increases 100 distinct kinds of atoms combine to form all the materials while potential and total energy decreases. in the universe. orbital quantum number l is 2(2l + 1). decreases, while wavelength of spectral line increases. E,  n=1 1 '  1 ' '  D YG  Thus, energy is released in this process (nuclear fusion). B. E. A U E,  E  E' E' ' E' ' ' 1 heavy nucleus, then binding energy per nucleon increases. n=2 '  ' '  ' ' '  n=4 n=3 E,   When two very light nuclei combines to form a relatively ID energy difference between the two successive energy level E,   Density of a nucleus is maximum at it's centre and decreases as we move outwards from the nucleus.  With the increase in principal quantum number the E'  E' '  E' ' ' E3  The maximum number of electrons in a subshell with 60 makes a transition from an + Fusion Fission + 1 A ' ' '  Rydberg constant is different for different elements R(=1.09  107 m–1) is the value of Rydberg constant  It may be noted that Plutonium is the best fuel as compared to the revolving electron. In other words, the compared to other fissionable material. It is because fission in nucleus is considered to be stationary. Plutonium can be initiated by both slow and fast neutrons. U when the nucleus is considered to be infinitely massive as In case, the nucleus is not infinitely massive or ST stationary, then the value of Rydberg constant is given as R' R where m is the mass of electron and M is the m 1 M mass of nucleus.  Atomic spectrum is a line spectrum Each atom has it's own characteristic allowed orbits depending upon the electronic configuration. Therefore photons emitted during transition of electrons from one Moreover it can be obtained from U 238.  Nuclear reactor is firstly devised by fermi.  Apsara was the first Indian nuclear reactor.  A type of reactor that can produce more fissile fuel than it consumes is the breeder reactor.  To achieve fusion in laboratory a device is used to confine the plasma, called Tokamak.  A test tube full of base nuclei will weight heavier than the Atomic and Nuclear Physics 1467 earth.  The nucleus of hydrogen contains only one proton. Therefore we may say that the proton is the nucleus of   = 1 + 2  T T1T2 T1  T2 hydrogen atom.  There are at least three varieties of neutranas, each with  If the relative abundance of isotopes in an element has a it's corresponding antineutrino; one is associated with beta ratio n1 : n2 whose atomic masses are m1 and m2 then atomic decay and the other two are associated with the decay of two n1 m1  n2 m 2 n1  n2 unstable particles, the muon and the tau particles. 60 mass of the element is M   Are all fusion reaction exoergic ?  No radioactive substance emits both  and  particles Fusion reaction between sufficiently light nuclei are E3 simultaneously. Also -rays are emitted after the emission of  or -particles. exoergic because the  -particles are not orbital electrons they come from massive, however B. E. decreases and fusion is endoergic A (i.e. it takes in energy rather than releasing it) ID nucleus. The neutron in the nucleus decays into proton and B. E. increases. If the nuclei are too A an electron. This electron is emitted out of the nucleus in the  The Zeeman effect is the spliting of atomic energy levels form of -rays. and the associated spectrum lines when the atoms are U  Activity per gm of a substance is known as specific activity. D YG The specific activity of 1 gm of radium – 226 is 1 Curie.  1 millicurie = 37 Rutherford  The activity of a radioactive substance decreases as the number of undecayed nuclei decreases with time.  Activity 1 Half life U  Half life and mean life of a substance doesn't change with time or with pressure, temperature etc. ST  If a nuclide can decay simultaneously by two different process which have decay constant 1 and 2, half life T1 and T2 and mean lives 1 and 2 respectively then  1 1, T1, 1 2 2, T2, 2 T  placed in a magnetic field. This effect confirms experimentally the quantization of angular momentum.