Structure of Atom PDF

Unit 2 structure of atom The rich diversity of chemical behaviour of different Objectives...

Unit 2 structure of atom The rich diversity of chemical behaviour of different Objectives elements can be traced to the differences in the internal structure of atoms of these elements. After studying this unit you will be able to know about the discovery of The existence of atoms has been proposed since the time electron, proton and neutron and of early Indian and Greek philosophers (400 B.C.) who their characteristics; were of the view that atoms are the fundamental building describe Thomson, Rutherford blocks of matter. According to them, the continued and Bohr atomic models; subdivisions of matter would ultimately yield atoms which would not be further divisible. The word ‘atom’ understand the important features has been derived from the Greek word ‘a-tomio’ which of the quantum mechanical model means ‘uncut-able’ or ‘non-divisible’. These earlier ideas of atom; were mere speculations and there was no way to test understand nature of them experimentally. These ideas remained dormant for electromagnetic radiation and a very long time and were revived again by scientists in Planck’s quantum theory; the nineteenth century. explain the photoelectric effect The atomic theory of matter was first proposed and describe features of atomic on a firm scientific basis by John Dalton, a British spectra; school teacher in 1808. His theory, called Dalton’s state the de Broglie relation and atomic theory, regarded the atom as the ultimate Heisenberg uncertainty principle; particle of matter (Unit 1). Dalton’s atomic theory was able to explain the law of conservation of mass, law of define an atomic orbital in terms constant composition and law of multiple proportion of quantum numbers; very successfully. However, it failed to explain the results state aufbau principle, Pauli of many experiments, for example, it was known that exclusion principle and Hund’s substances like glass or ebonite when rubbed with silk rule of maximum multiplicity; and or fur get electrically charged. write the electronic configurations In this unit we start with the experimental observations of atoms. made by scientists towards the end of nineteenth and beginning of twentieth century. These established that atoms are made of sub-atomic particles, i.e., electrons, protons and neutrons — a concept very different from that of Dalton. 2024-25 Unit 2.indd 29 9/9/2022 4:28:07 PM  30 chemistry 2.1 Discovery of Sub-atomic Particles An insight into the structure of atom was obtained from the experiments on electrical discharge through gases. Before we discuss these results we need to keep in mind a basic rule regarding the behaviour of charged particles : “Like charges repel each other and unlike charges attract each other”. Fig. 2.1(a) A cathode ray discharge tube 2.1.1 Discovery of Electron In 1830, Michael Faraday showed that if electricity is passed through a solution of an electrolyte, chemical reactions occurred at the electrodes, which resulted in the liberation and deposition of matter at the electrodes. He formulated certain laws which you will study in Class XII. These results suggested the particulate nature of electricity. Fig. 2.1(b) A cathode ray discharge tube with In mid 1850s many scientists mainly perforated anode Faraday began to study electrical discharge in partially evacuated tubes, known as The results of these experiments are cathode ray discharge tubes. It is depicted summarised below. in Fig. 2.1. A cathode ray tube is made of (i) The cathode rays start from cathode and move towards the anode. glass containing two thin pieces of metal, called electrodes, sealed in it. The electrical (ii) These rays themselves are not visible but their behaviour can be observed discharge through the gases could be with the help of certain kind of materials observed only at very low pressures and at (fluorescent or phosphorescent) which very high voltages. The pressure of different glow when hit by them. Television gases could be adjusted by evacuation of the picture tubes are cathode ray tubes glass tubes. When sufficiently high voltage and television pictures result due to is applied across the electrodes, current fluorescence on the television screen starts flowing through a stream of particles coated with certain fluorescent or moving in the tube from the negative phosphorescent materials. electrode (cathode) to the positive electrode (iii) In the absence of electrical or magnetic field, these rays travel in straight lines (anode). These were called cathode rays or (Fig. 2.2). cathode ray particles. The flow of current (iv) In the presence of electrical or magnetic from cathode to anode was further checked field, the behaviour of cathode rays are by making a hole in the anode and coating similar to that expected from negatively the tube behind anode with phosphorescent charged particles, suggesting that material zinc sulphide. When these rays, the cathode rays consist of negatively after passing through anode, strike the zinc charged particles, called electrons. sulphide coating, a bright spot is developed (v) The characteristics of cathode rays on the coating [Fig. 2.1(b)]. (electrons) do not depend upon the 2024-25 Unit 2.indd 30 9/9/2022 4:28:08 PM  structure of atom 31 material of electrodes and the nature of (iii) the strength of the electrical or magnetic the gas present in the cathode ray tube. field — the deflection of electrons from its Thus, we can conclude that electrons are original path increases with the increase basic constituent of all the atoms. in the voltage across the electrodes, or the strength of the magnetic field. 2.1.2 Charge to Mass Ratio of Electron By carrying out accurate measurements In 1897, British physicist J.J. Thomson on the amount of deflections observed by measured the ratio of electrical charge (e) to the electrons on the electric field strength or the mass of electron (me ) by using cathode magnetic field strength, Thomson was able to ray tube and applying electrical and magnetic determine the value of e/me as: field perpendicular to each other as well as to the path of electrons (Fig. 2.2). When only = 1.758820 × 1011 C kg–1 (2.1) electric field is applied, the electrons deviate from their path and hit the cathode ray tube Where me is the mass of the electron in kg at point A (Fig. 2.2). Similarly when only and e is the magnitude of the charge on the magnetic field is applied, electron strikes electron in coulomb (C). Since electrons are the cathode ray tube at point C. By carefully negatively charged, the charge on electron balancing the electrical and magnetic field is –e. strength, it is possible to bring back the electron to the path which is followed in the 2.1.3 Charge on the Electron absence of electric or magnetic field and they R.A. Millikan (1868-1953) devised a method hit the screen at point B. Thomson argued known as oil drop experiment (1906-14), that the amount of deviation of the particles to determine the charge on the electrons. from their path in the presence of electrical He found the charge on the electron to be or magnetic field depends upon: – 1.6 × 10–19 C. The present accepted value of electrical charge is – 1.602176 × 10–19 C. The (i) the magnitude of the negative charge on mass of the electron (me) was determined by the particle, greater the magnitude of combining these results with Thomson’s value the charge on the particle, greater is the of e/me ratio. interaction with the electric or magnetic field and thus greater is the deflection. (ii) the mass of the particle — lighter the particle, greater the deflection. = 9.1094×10–31 kg (2.2) Fig. 2.2 The apparatus to determine the charge to the mass ratio of electron 2024-25 Unit 2.indd 31 9/9/2022 4:28:08 PM  32 chemistry 2.1.4 Discovery of Protons and Neutrons Millikan’s Oil Drop Method Electrical discharge carried out in the modified cathode ray tube led to the discovery of canal In this method, oil droplets in the form of rays carrying positively charged particles. The mist, produced by the atomiser, were allowed characteristics of these positively charged to enter through a tiny hole in the upper particles are listed below. plate of electrical condenser. The downward motion of these droplets was viewed through (i) Unlike cathode rays, mass of positively the telescope, equipped with a micrometer charged particles depends upon the eye piece. By measuring the rate of fall of nature of gas present in the cathode these droplets, Millikan was able to measure ray tube. These are simply the positively the mass of oil droplets. The air inside the charged gaseous ions. chamber was ionized by passing a beam of (ii) The charge to mass ratio of the particles X-rays through it. The electrical charge on depends on the gas from which these these oil droplets was acquired by collisions with gaseous ions. The fall of these charged originate. oil droplets can be retarded, accelerated or (iii) Some of the positively charged particles made stationary depending upon the charge carry a multiple of the fundamental unit on the droplets and the polarity and strength of electrical charge. of the voltage applied to the plate. By (iv) The behaviour of these particles in the carefully measuring the effects of electrical magnetic or electrical field is opposite field strength on the motion of oil droplets, to that observed for electron or cathode Millikan concluded that the magnitude of electrical charge, q, on the droplets is always rays. an integral multiple of the electrical charge, The smallest and lightest positive ion e, that is, q = n e, where n = 1, 2, 3.... was obtained from hydrogen and was called proton. This positively charged particle was characterised in 1919. Later, a need was felt for the presence of electrically neutral particle as one of the constituent of atom. These particles were discovered by Chadwick (1932) by bombarding a thin sheet of beryllium by α-particles. When electrically neutral particles having a mass slightly greater than that of protons were emitted. He named these particles as neutrons. The important properties of all these fundamental particles are given in Table 2.1. Fig. 2.3 The Millikan oil drop apparatus for 2.2 Atomic Models measuring charge ‘e’. In chamber, Observations obtained from the experiments the forces acting on oil drop are: mentioned in the previous sections have gravitational, electrostatic due to electrical field and a viscous drag suggested that Dalton’s indivisible atom is force when the oil drop is moving. composed of sub-atomic particles carrying positive and negative charges. The major problems before the scientists after the to explain the formation of different discovery of sub-atomic particles were: kinds of molecules by the combination of different atoms and, to account for the stability of atom, to compare the behaviour of elements to understand the origin and nature of the characteristics of electromagnetic in terms of both physical and chemical radiation absorbed or emitted by atoms. properties, 2024-25 Unit 2.indd 32 9/9/2022 4:28:08 PM  structure of atom 33 Table 2.1 Properties of Fundamental Particles Name Symbol Absolute Relative Mass/kg Mass/u Approx. charge/C charge mass/u Electron e – 1.602176×10–19 –1 9.109382×10–31 0.00054 0 Proton p + 1.602176×10–19 +1 1.6726216×10–27 1.00727 1 Neutron n 0 0 1.674927×10–27 1.00867 1 Different atomic models were proposed to explain the distributions of these charged In the later half of the nineteenth century particles in an atom. Although some of these different kinds of rays were discovered, models were not able to explain the stability besides those mentioned earlier. Wilhalm of atoms, two of these models, one proposed Röentgen (1845-1923) in 1895 showed by J.J. Thomson and the other proposed by that when electrons strike a material in Ernest Rutherford are discussed below. the cathode ray tubes, produce rays which can cause fluorescence in the fluorescent 2.2.1 Thomson Model of Atom materials placed outside the cathode ray J. J. Thomson, in 1898, proposed that an tubes. Since Röentgen did not know the atom possesses a spherical shape (radius nature of the radiation, he named them approximately 10–10 m) in which the positive X-rays and the name is still carried on. It was charge is uniformly distributed. The electrons noticed that X-rays are produced effectively are embedded into it in such a manner as to give the most stable electrostatic arrangement when electrons strike the dense metal anode, (Fig. 2.4). Many different names are given called targets. These are not deflected by the to this model, for example, plum pudding, electric and magnetic fields and have a very raisin pudding or watermelon. This model high penetrating power through the matter and that is the reason that these rays are used to study the interior of the objects. These rays are of very short wavelengths (∼0.1 nm) and possess electro-magnetic character (Section 2.3.1). Henri Becqueral (1852-1908) observed that there are certain elements which emit radiation on their own and named this Fig.2.4 Thomson model of atom phenomenon as radioactivity and the can be visualised as a pudding or watermelon elements known as radioactive elements. of positive charge with plums or seeds This field was developed by Marie Curie, (electrons) embedded into it. An important Piere Curie, Rutherford and Fredrick Soddy. feature of this model is that the mass of the It was observed that three kinds of rays i.e., atom is assumed to be uniformly distributed α, β- and γ-rays are emitted. Rutherford over the atom. Although this model was able found that α-rays consists of high energy to explain the overall neutrality of the atom, particles carrying two units of positive charge but was not consistent with the results of later and four unit of atomic mass. He concluded experiments. Thomson was awarded Nobel that α- particles are helium nuclei as when α- Prize for physics in 1906, for his theoretical particles combined with two electrons yielded and experimental investigations on the helium gas. β-rays are negatively charged conduction of electricity by gases. 2024-25 Unit 2.indd 33 9/9/2022 4:28:08 PM  34 chemistry represented in Fig. 2.5. A stream of high particles similar to electrons. The γ-rays energy α–particles from a radioactive source are high energy radiations like X-rays, are was directed at a thin foil (thickness ∼ 100 nm) neutral in nature and do not consist of of gold metal. The thin gold foil had a circular particles. As regards penetrating power, fluorescent zinc sulphide screen around it. α-particles are the least, followed by β-rays Whenever α–particles struck the screen, a (100 times that of α–particles) and γ-rays tiny flash of light was produced at that point. (1000 times of that α-particles). The results of scattering experiment were quite unexpected. According to Thomson 2.2.2 Rutherford’s Nuclear Model of Atom model of atom, the mass of each gold atom in the foil should have been spread evenly Rutherford and his students (Hans Geiger over the entire atom, and α–particles had and Ernest Marsden) bombarded very thin enough energy to pass directly through such a gold foil with α–particles. Rutherford’s famous uniform distribution of mass. It was expected –particle scattering experiment is that the particles would slow down and change directions only by a small angles as they passed through the foil. It was observed that: (i) most of the α–particles passed through the gold foil undeflected. (ii) a small fraction of the α–particles was deflected by small angles. (iii) a very few α–particles (∼1 in 20,000) bounced back, that is, were deflected by A. Rutherford’s scattering experiment nearly 180°. On the basis of the observations, Rutherford drew the following conclusions regarding the structure of atom: (i) Most of the space in the atom is empty as most of the α–particles passed through the foil undeflected. (ii) A few positively charged α–particles were deflected. The deflection must be due to enormous repulsive force showing that the positive charge of the atom is not spread throughout the atom as Thomson had presumed. The positive charge has to be concentrated in a very small volume that repelled and deflected the positively charged α–particles. B. Schematic molecular view of the gold foil (iii) Calculations by Rutherford showed that the volume occupied by the nucleus Fig. 2.5 Schematic view of Rutherford’s scattering experiment. When a beam is negligibly small as compared to the of alpha () particles is “shot” at a thin total volume of the atom. The radius of gold foil, most of them pass through the atom is about 10–10 m, while that of without much effect. Some, however, nucleus is 10–15 m. One can appreciate are deflected. this difference in size by realising that if 2024-25 Unit 2.indd 34 9/9/2022 4:28:08 PM  structure of atom 35 a cricket ball represents a nucleus, then The total number of nucleons is termed as the radius of atom would be about 5 km. mass number (A) of the atom. On the basis of above observations and mass number (A) = number of protons (Z ) conclusions, Rutherford proposed the nuclear + number of model of atom. According to this model: neutrons (n) (2.4) (i) The positive charge and most of the mass 2.2.4 Isobars and Isotopes of the atom was densely concentrated in The composition of any atom can be extremely small region. This very small represented by using the normal element portion of the atom was called nucleus symbol (X) with super-script on the left hand by Rutherford. side as the atomic mass number (A) and (ii) The nucleus is surrounded by electrons subscript (Z ) on the left hand side as the that move around the nucleus with a atomic number (i.e., AZ X). very high speed in circular paths called orbits. Thus, Rutherford’s model of atom Isobars are the atoms with same mass resembles the solar system in which the number but different atomic number for nucleus plays the role of sun and the example, 146 C and 14 7 N. On the other hand, electrons that of revolving planets. atoms with identical atomic number but different atomic mass number are known (iii) Electrons and the nucleus are held as Isotopes. In other words (according to together by electrostatic forces of equation 2.4), it is evident that difference attraction. between the isotopes is due to the presence 2.2.3 Atomic Number and Mass Number of different number of neutrons present in The presence of positive charge on the nucleus the nucleus. For example, considering of is due to the protons in the nucleus. As hydrogen atom again, 99.985% of hydrogen established earlier, the charge on the proton atoms contain only one proton. This isotope is is equal but opposite to that of electron. The called protium (11H). Rest of the percentage of number of protons present in the nucleus is hydrogen atom contains two other isotopes, equal to atomic number (Z ). For example, the the one containing 1 proton and 1 neutron number of protons in the hydrogen nucleus is called deuterium (12D, 0.015%) and the is 1, in sodium atom it is 11, therefore their other one possessing 1 proton and 2 neutrons atomic numbers are 1 and 11 respectively. is called tritium (13T ). The latter isotope is In order to keep the electrical neutrality, found in trace amounts on the earth. Other the number of electrons in an atom is equal examples of commonly occuring isotopes are: to the number of protons (atomic number, carbon atoms containing 6, 7 and 8 neutrons Z ). For example, number of electrons in besides 6 protons ( 12 13 14 ); chlorine 6 C, 6 C, 6 C hydrogen atom and sodium atom are 1 and atoms containing 18 and 20 neutrons besides 11 respectively. 17 protons ( 17 35 37 Cl, 17 Cl ). Atomic number (Z) = number of protons in Lastly an important point to mention the nucleus of an atom regarding isotopes is that chemical properties = number of electrons of atoms are controlled by the number of in a nuetral atom (2.3) electrons, which are determined by the number While the positive charge of the nucleus of protons in the nucleus. Number of neutrons is due to protons, the mass of the nucleus, present in the nucleus have very little effect due to protons and neutrons. As discussed on the chemical properties of an element. earlier protons and neutrons present in the Therefore, all the isotopes of a given element nucleus are collectively known as nucleons. show same chemical behaviour. 2024-25 Unit 2.indd 35 9/9/2022 4:28:09 PM  36 chemistry of the massive sun and the electrons being Problem 2.1 similar to the lighter planets. When classical Calculate the number of protons, mechanics* is applied to the solar system, it neutrons and electrons in 80 35 Br. shows that the planets describe well-defined Solution orbits around the sun. The gravitational force between the planets is given by the expression In this case, 80 35 Br , Z = 35, A = 80, species  m1m 2  is neutral  G. 2  where m1 and m2 are the masses, r Number of protons = number of electrons = Z = 35 r is the distance of separation of the masses and G is the gravitational constant. The theory Number of neutrons = 80 – 35 = 45, can also calculate precisely the planetary (equation 2.4) orbits and these are in agreement with the Problem 2.2 experimental measurements. The number of electrons, protons and The similarity between the solar system neutrons in a species are equal to 18, 16 and nuclear model suggests that electrons and 16 respectively. Assign the proper should move around the nucleus in well symbol to the species. defined orbits. Further, the coulomb force Solution (kq1q2/r2 where q1 and q2 are the charges, r is the distance of separation of the charges The atomic number is equal to and k is the proportionality constant) between number of protons = 16. The element is sulphur (S). electron and the nucleus is mathematically similar to the gravitational force. However, Atomic mass number = number of when a body is moving in an orbit, it protons + number of neutrons undergoes acceleration even if it is moving = 16 + 16 = 32 with a constant speed in an orbit because Species is not neutral as the number of of changing direction. So an electron in the protons is not equal to electrons. It is nuclear model describing planet like orbits anion (negatively charged) with charge is under acceleration. According to the equal to excess electrons = 18 – 16 = 2. electromagnetic theory of Maxwell, charged Symbol is. A particles when accelerated should emit Note : Before using the notation Z X, electromagnetic radiation (This feature does find out whether the species is a neutral not exist for planets since they are uncharged). atom, a cation or an anion. If it is a Therefore, an electron in an orbit will emit neutral atom, equation (2.3) is valid, i.e., radiation, the energy carried by radiation number of protons = number of electrons comes from electronic motion. The orbit will = atomic number. If the species is an ion, determine whether the number of thus continue to shrink. Calculations show protons are larger (cation, positive ion) that it should take an electron only 10–8 s or smaller (anion, negative ion) than the to spiral into the nucleus. But this does number of electrons. Number of neutrons not happen. Thus, the Rutherford model is always given by A–Z, whether the cannot explain the stability of an atom. species is neutral or ion. If the motion of an electron is described on the basis of the classical mechanics and 2.2.5 Drawbacks of Rutherford Model electromagnetic theory, you may ask that As you have learnt above, Rutherford nuclear since the motion of electrons in orbits is model of an atom is like a small scale solar leading to the instability of the atom, then system with the nucleus playing the role why not consider electrons as stationary * Classical mechanics is a theoretical science based on Newton’s laws of motion. It specifies the laws of motion of macroscopic objects. 2024-25 Unit 2.indd 36 9/9/2022 4:28:09 PM  structure of atom 37 around the nucleus. If the electrons were was developed in the early 1870’s by James stationary, electrostatic attraction between Clerk Maxwell, which was experimentally the dense nucleus and the electrons would confirmed later by Heinrich Hertz. Here, we pull the electrons toward the nucleus to will learn some facts about electromagnetic form a miniature version of Thomson’s model radiations. of atom. James Maxwell (1870) was the first to Another serious drawback of the give a comprehensive explanation about the Rutherford model is that it says nothing interaction between the charged bodies and about distribution of the electrons around the the behaviour of electrical and magnetic nucleus and the energies of these electrons. fields on macroscopic level. He suggested 2.3 Developments Leading to the that when electrically charged particle moves Bohr’s Model of Atom under accelaration, alternating electrical and magnetic fields are produced and transmitted. Historically, results observed from the studies These fields are transmitted in the forms of interactions of radiations with matter have of waves called electromagnetic waves or provided immense information regarding electromagnetic radiation. the structure of atoms and molecules. Neils Bohr utilised these results to improve upon Light is the form of radiation known from the model proposed by Rutherford. Two early days and speculation about its nature developments played a major role in the dates back to remote ancient times. In earlier formulation of Bohr’s model of atom. These days (Newton) light was supposed to be made were: of particles (corpuscules). It was only in the 19th century when wave nature of light was (i) Dual character of the electromagnetic established. radiation which means that radiations possess both wave like and particle like Maxwell was again the first to reveal that properties, and light waves are associated with oscillating electric and magnetic character (Fig. 2.6). (ii) Experimental results regarding atomic spectra. First, we will discuss about the duel nature of electromagnetic radiations. Experimental results regarding atomic spectra will be discussed in Section 2.4. 2.3.1 Wave Nature of Electromagnetic Radiation In the mid-nineteenth century, physicists actively studied absorption and emission of radiation by heated objects. These are called Fig.2.6 The electric and magnetic field thermal radiations. They tried to find out of components of an electromagnetic what the thermal radiation is made. It is now wave. These components have the a well-known fact that thermal radiations same wavelength, frequency, speed consist of electromagnetic waves of various and amplitude, but they vibrate in two frequencies or wavelengths. It is based on mutually perpendicular planes. a number of modern concepts, which were unknown in the mid-nineteenth century. Although electromagnetic wave motion is First active study of thermal radiation laws complex in nature, we will consider here only occured in the 1850’s and the theory of a few simple properties. electromagnetic waves and the emission of (i) The oscillating electric and magnetic such waves by accelerating charged particles fields produced by oscillating charged 2024-25 Unit 2.indd 37 9/9/2022 4:28:10 PM  38 chemistry particles are perpendicular to each (iv) Different kinds of units are used to other and both are perpendicular to the represent electromagnetic radiation. direction of propagation of the wave. Simplified picture of electromagnetic These radiations are characterised by wave is shown in Fig. 2.6. the properties, namely, frequency (ν ) and (ii) Unlike sound waves or waves produced wavelength (λ). in water, electromagnetic waves do The SI unit for frequency (ν) is hertz not require medium and can move in (Hz, s–1), after Heinrich Hertz. It is defined as vacuum. the number of waves that pass a given point (iii) It is now well established that there in one second. are many types of electromagnetic radiations, which differ from one Wavelength should have the units of another in wavelength (or frequency). length and as you know that the SI units of These constitute what is called length is meter (m). Since electromagnetic electromagnetic spectrum (Fig. 2.7). radiation consists of different kinds of waves Different regions of the spectrum are of much smaller wavelengths, smaller units identified by different names. Some are used. Fig. 2.7 shows various types of examples are: radio frequency region electro-magnetic radiations which differ from around 106 Hz, used for broadcasting; one another in wavelengths and frequencies. microwave region around 1010 Hz used for radar; infrared region around 1013 In vaccum all types of electromagnetic Hz used for heating; ultraviolet region radiations, regardless of wavelength, travel at around 1016Hz a component of sun’s the same speed, i.e., 3.0 × 108 m s–1 (2.997925 radiation. The small portion around 1015 × 108 ms–1, to be precise). This is called speed Hz, is what is ordinarily called visible of light and is given the symbol ‘c’. The light. It is only this part which our eyes frequency (ν ), wavelength (λ) and velocity of can see (or detect). Special instruments are required to detect non-visible light (c) are related by the equation (2.5). radiation. c = ν λ (2.5) (a) (b) Fig. 2.7 (a) The spectrum of electromagnetic radiation. (b) Visible spectrum. The visible region is only a small part of the entire spectrum. 2024-25 Unit 2.indd 38 9/9/2022 4:28:10 PM  structure of atom 39 The other commonly used quantity Frequency of red light specially in spectroscopy, is the wavenumber ( ). It is defined as the number of wavelengths per unit length. Its units are reciprocal of ν= = 4.00 × 1014 Hz wavelength unit, i.e., m–1. However commonly The range of visible spectrum is from used unit is cm–1 (not SI unit). 4.0 × 1014 to 7.5 × 1014 Hz in terms of Problem 2.3 frequency units. The Vividh Bharati station of All India Problem 2.5 Radio, Delhi, broadcasts on a frequency Calculate (a) wavenumber and (b) of 1,368 kHz (kilo hertz). Calculate frequency of yellow radiation having the wavelength of the electromagnetic wavelength 5800 Å. radiation emitted by transmitter. Which part of the electromagnetic spectrum Solution does it belong to? (a) Calculation of wavenumber ( ) Solution λ=5800Å = 5800 × 10–8 cm = 5800 × 10–10 m The wavelength, λ, is equal to c/ν, where c is the speed of electromagnetic radiation in vacuum and ν is the frequency. Substituting the given values, we have c  v (b) Calculation of the frequency (ν ) 2.3.2 Particle Nature of Electromagnetic Radiation: Planck’s Quantum This is a characteristic radiowave Theory wavelength. Some of the experimental phenomenon such as diffraction* and interference** can Problem 2.4 be explained by the wave nature of the The wavelength range of the visible electromagnetic radiation. However, following spectrum extends from violet (400 nm) to are some of the observations which could red (750 nm). Express these wavelengths not be explained with the help of even the in frequencies (Hz). (1nm = 10–9 m) electromagentic theory of 19th century Solution physics (known as classical physics): Using equation 2.5, frequency of violet (i) the nature of emission of radiation from light hot bodies (black-body radiation) (ii) ejection of electrons from metal surface when radiation strikes it (photoelectric effect) = 7.50 × 1014 Hz (iii) variation of heat capacity of solids as a function of temperature * Diffraction is the bending of wave around an obstacle. ** Interference is the combination of two waves of the same or different frequencies to give a wave whose distribution at each point in space is the algebraic or vector sum of disturbances at that point resulting from each interfering wave. 2024-25 Unit 2.indd 39 9/9/2022 4:28:10 PM  40 chemistry (iv) Line spectra of atoms with special entering the hole will be reflected by the cavity reference to hydrogen. walls and will be eventually absorbed by the These phenomena indicate that the system walls. A black body is also a perfect radiator of can take energy only in discrete amounts. radiant energy. Furthermore, a black body is All possible energies cannot be taken up or in thermal equilibrium with its surroundings. radiated. It radiates same amount of energy per unit area as it absorbs from its surrounding in It is noteworthy that the first concrete any given time. The amount of light emitted explanation for the phenomenon of the black (intensity of radiation) from a black body body radiation mentioned above was given and its spectral distribution depends only by Max Planck in 1900. Let us first try to on its temperature. At a given temperature, understand this phenomenon, which is given intensity of radiation emitted increases below: with the increase of wavelength, reaches a Ho t o b j e c t s e m i t e l e c t r o m a g n e t i c maximum value at a given wavelength and radiations over a wide range of wavelengths. then starts decreasing with further increase of At high temperatures, an appreciable wavelength, as shown in Fig. 2.8. Also, as the proportion of radiation is in the visible temperature increases, maxima of the curve region of the spectrum. As the temperature shifts to short wavelength. Several attempts is raised, a higher proportion of short were made to predict the intensity of radiation wavelength (blue light) is generated. For as a function of wavelength. example, when an iron rod is heated in a But the results of the above experiment furnace, it first turns to dull red and then could not be explained satisfactorily on progressively becomes more and more red the basis of the wave theory of light. Max as the temperature increases. As this is Planck arrived at a satisfactory relationship heated further, the radiation emitted becomes white and then becomes blue as the temperature becomes very high. This means that red radiation is most intense at a particular temperature and the blue radiation is more intense at another temperature. This means intensities of radiations of different wavelengths emitted by hot body depend upon its temperature. By late 1850’s it was known that objects made of different material and kept at different temperatures emit different amount of radiation. Also, when the surface of an object is irradiated with light (electromagnetic radiation), a part of radiant energy is generally reflected as such, a part Fig. 2.8 Wavelength-intensity relationship is absorbed and a part of it is transmitted. The reason for incomplete absorption is that ordinary objects are as a rule imperfect absorbers of radiation. An ideal body, which emits and absorbs radiations of all frequencies uniformly, is called a black body and the radiation emitted by such a body is called black body radiation. In practice, no such body exists. Carbon black approximates fairly closely to black body. A good physical approximation to a black body is a cavity with a tiny hole, which has no other opening. Any ray Fig. 2.8(a) Black body 2024-25 Unit 2.indd 40 9/9/2022 4:28:10 PM  structure of atom 41 by making an assumption that absorption and emmission of radiation arises from Max Planck (1858–1947) oscillator i.e., atoms in the wall of black Max Planck, a German physicist, body. Their frequency of oscillation is received his Ph.D in theoretical changed by interaction with oscilators of physics from the University of electromagnetic radiation. Planck assumed Munich in 1879. In 1888, he that radiation could be sub-divided into was appointed Director of the discrete chunks of energy. He suggested that Institute of Theoretical Physics atoms and molecules could emit or absorb at the University of Berlin. energy only in discrete quantities and not Planck was awarded the Nobel Prize in Physics in a continuous manner. He gave the name in 1918 for his quantum theory. Planck also made quantum to the smallest quantity of energy significant contributions in thermodynamics and that can be emitted or absorbed in the form other areas of physics. of electromagnetic radiation. The energy (E) of a quantum of radiation is proportional Photoelectric Effect to its frequency (ν) and is expressed by In 1887, H. Hertz performed a very interesting equation (2.6). experiment in which electrons (or electric E = hυ (2.6) current) were ejected when certain metals The proportionality constant, ‘h’ is known (for example potassium, rubidium, caesium as Planck’s constant and has the value etc.) were exposed to a beam of light as shown 6.626×10–34 J s. in Fig. 2.9. The phenomenon is called Photoelectric effect. The results observed With this theory, Planck was able to explain in this experiment were: the distribution of intensity in the radiation from black body as a function of frequency or (i) The electrons are ejected from the metal wavelength at different temperatures. surface as soon as the beam of light strikes the surface, i.e., there is no time Quantisation has been compared to lag between the striking of light beam and standing on a staircase. A person can stand the ejection of electrons from the metal on any step of a staircase, but it is not possible surface. for him/her to stand in between the two steps. The energy can take any one of the values (ii) The number of electrons ejected is from the following set, but cannot take on any proportional to the intensity or brightness values between them. of light. E = 0, hυ, 2hυ , 3hυ....nhυ..... (iii) For each metal, there is a characteristic minimum frequency, ν 0 (also known as threshold frequency) below which photoelectric effect is not observed. At a frequency ν >ν0, the ejected electrons come out with certain kinetic energy. The kinetic energies of these electrons increase with the increase of frequency of the light used. All the above results could not be explained on the basis of laws of classical physics. Fig.2.9 Equipment for studying the photoelectric According to latter, the energy content of the effect. Light of a particular frequency beam of light depends upon the brightness of strikes a clean metal surface inside a the light. In other words, number of electrons vacuum chamber. Electrons are ejected from the metal and are counted by a ejected and kinetic energy associated with detector that measures their kinetic them should depend on the brightness of light. energy. It has been observed that though the number 2024-25 Unit 2.indd 41 9/9/2022 4:28:11 PM  42 chemistry Table 2.2 Values of Work Function (W0) for a Few Metals Metal Li Na K Mg Cu Ag W0 /eV 2.42 2.3 2.25 3.7 4.8 4.3 of electrons ejected does depend upon the the minimum energy required to eject the brightness of light, the kinetic energy of the electron is hν0 (also called work function, ejected electrons does not. For example, red W0 ; Table 2.2), then the difference in energy light [ν = (4.3 to 4.6) × 1014 Hz] of any brightness (hν – hν0 ) is transferred as the kinetic energy of (intensity) may shine on a piece of potassium the photoelectron. Following the conservation metal for hours but no photoelectrons are of energy principle, the kinetic energy of the ejected. But, as soon as even a very weak ejected electron is given by the equation 2.7. yellow light (ν = 5.1–5.2 × 1014 Hz) shines on the potassium metal, the photoelectric effect (2.7) is observed. The threshold frequency (ν0) for where me is the mass of the electron and v is the potassium metal is 5.0×1014 Hz. velocity associated with the ejected electron. Einstein (1905) was able to explain the Lastly, a more intense beam of light consists photoelectric effect using Planck’s quantum of larger number of photons, consequently the theory of electromagnetic radiation as a number of electrons ejected is also larger as starting point. compared to that in an experiment in which a beam of weaker intensity of light is employed. Albert Einstein, a German born American physicist, is regarded Dual Behaviour of Electromagnetic by many as one of the two great Radiation physicists the world has known (the other is Isaac Newton). His The particle nature of light posed a dilemma for three research papers (on special scientists. On the one hand, it could explain relativity, Brownian motion and the black body radiation and photoelectric the photoelectric effect) which Albert Einstein effect satisfactorily but on the other hand, he published in 1905, while he (1879–1955) was employed as a technical it was not consistent with the known wave assistant in a Swiss patent office in Berne have behaviour of light which could account for the profoundly influenced the development of physics. phenomena of interference and diffraction. He received the Nobel Prize in Physics in 1921 for The only way to resolve the dilemma was his explanation of the photoelectric effect. to accept the idea that light possesses both particle and wave-like properties, i.e., Shining a beam of light on to a metal surface can, therefore, be viewed as shooting light has dual behaviour. Depending on a beam of particles, the photons. When a the experiment, we find that light behaves photon of sufficient energy strikes an electron either as a wave or as a stream of particles. in the atom of the metal, it transfers its energy Whenever radiation interacts with matter, it instantaneously to the electron during the displays particle like properties in contrast collision and the electron is ejected without to the wavelike properties (interference any time lag or delay. Greater the energy and diffraction), which it exhibits when it possessed by the photon, greater will be propagates. This concept was totally alien to transfer of energy to the electron and greater the way the scientists thought about matter the kinetic energy of the ejected electron. In and radiation and it took them a long time to other words, kinetic energy of the ejected become convinced of its validity. It turns out, electron is proportional to the frequency as you shall see later, that some microscopic of the electromagnetic radiation. Since the particles like electrons also exhibit this wave- striking photon has energy equal to hν and particle duality. 2024-25 Unit 2.indd 42 9/9/2022 4:28:11 PM  structure of atom 43 Problem 2.6 Solution Calculate energy of one mole of photons The energy (E) of a 300 nm photon is of radiation whose frequency is 5 ×1014 given by Hz. Solution Energy (E) of one photon is given by the expression = 6.626 × 10–19 J E = hν The energy of one mole of photons h = 6.626 ×10–34 J s = 6.626 ×10–19 J × 6.022 × 1023 mol–1 ν = 5×10 14 s (given) –1 = 3.99 × 105 J mol–1 E = (6.626 ×10 –34 J s) × (5 ×10 14 s ) –1 The minimum energy needed to remove = 3.313 ×10 –19 J one mole of electrons from sodium Energy of one mole of photons = (3.99 –1.68) 105 J mol–1 = (3.313 ×10–19 J) × (6.022 × 1023 mol–1) = 2.31 × 105 J mol–1 = 199.51 kJ mol–1 The minimum energy for one electron Problem 2.7 A 100 watt bulb emits monochromatic light of wavelength 400 nm. Calculate the number of photons emitted per second This corresponds to the wavelength by the bulb. hc = Solution E 6.626 10 34 J s 3.0 108 m s 1 Power of the bulb = 100 watt = 3.84 10 19 J = 100 J s–1 = 517 nm Energy of one photon E = hν = hc/λ (This corresponds to green light) 6.626  10 34 J s  3  108 m s 1 Problem 2.9 = 400  10 9 m The threshold frequency ν0 for a metal is = 4.969 × 10 –19 J 7.0 ×1014 s–1. Calculate the kinetic energy of an electron emitted when radiation of Number of photons emitted frequency ν =1.0 ×1015 s–1 hits the metal. 100 J s 1 Solution  2.012  1020 s 1 4.969  10 19 J According to Einstein’s equation Problem 2.8 Kinetic energy = ½ mev2=h(ν – ν0 ) When electromagnetic radiation of = (6.626 × 10–34 J s) (1.0 × 1015 s–1 – 7.0 wavelength 300 nm falls on the surface ×1014 s–1) of sodium, electrons are emitted with a = (6.626 × 10–34 J s) (10.0 × 1014 s–1 – 7.0 kinetic energy of 1.68 ×105 J mol–1. What ×1014 s–1) is the minimum energy needed to remove = (6.626 × 10–34 J s) × (3.0 × 1014 s–1) an electron from sodium? What is the maximum wavelength that will cause a = 1.988 × 10–19 J photoelectron to be emitted? 2024-25 Unit 2.indd 43 9/9/2022 4:28:11 PM  44 chemistry 2.3.3 Evidence for the quantized* spectrum. A continuum of radiation is passed Electronic Energy Levels: Atomic through a sample which absorbs radiation of spectra certain wavelengths. The missing wavelength The speed of light depends upon the nature which corresponds to the radiation absorbed of the medium through which it passes. As a by the matter, leave dark spaces in the bright result, the beam of light is deviated or refracted continuous spectrum. from its original path as it passes from one The study of emission or absorption medium to another. It is observed that when spectra is referred to as spectroscopy. The a ray of white light is passed through a prism, spectrum of the visible light, as discussed the wave with shorter wavelength bends more above, was continuous as all wavelengths (red than the one with a longer wavelength. Since to violet) of the visible light are represented in ordinary white light consists of waves with the spectra. The emission spectra of atoms in all the wavelengths in the visible range, a ray the gas phase, on the other hand, do not show of white light is spread out into a series of a continuous spread of wavelength from red coloured bands called spectrum. The light of to violet, rather they emit light only at specific red colour which has longest wavelength is wavelengths with dark spaces between them. deviated the least while the violet light, which Such spectra are called line spectra or has shortest wavelength is deviated the most. atomic spectra because the emitted radiation The spectrum of white light, that we can is identified by the appearance of bright lines see, ranges from violet at 7.50 × 1014 Hz to in the spectra (Fig. 2.10 page 45). red at 4×1014 Hz. Such a spectrum is called Line emission spectra are of great continuous spectrum. Continuous because interest in the study of electronic structure. violet merges into blue, blue into green and Each element has a unique line emission so on. A similar spectrum is produced when spectrum. The characteristic lines in atomic a rainbow forms in the sky. Remember that spectra can be used in chemical analysis to visible light is just a small portion of the identify unknown atoms in the same way electromagnetic radiation (Fig.2.7). When as fingerprints are used to identify people. electromagnetic radiation interacts with The exact matching of lines of the emission matter, atoms and molecules may absorb spectrum of the atoms of a known element energy and reach to a higher energy state. With with the lines from an unknown sample higher energy, these are in an unstable state. quickly establishes the identity of the latter, For returning to their normal (more stable, German chemist, Robert Bunsen (1811-1899) lower energy states) energy state, the atoms was one of the first investigators to use line and molecules emit radiations in various spectra to identify elements. regions of the electromagnetic spectrum. Elements like rubidium (Rb), caesium (Cs) thallium (Tl), indium (In), gallium (Ga) and Emission and Absorption Spectra scandium (Sc) were discovered when their The spectrum of radiation emitted by a minerals were analysed by spectroscopic substance that has absorbed energy is called methods. The element helium (He) was an emission spectrum. Atoms, molecules or discovered in the sun by spectroscopic method. ions that have absorbed radiation are said Line Spectrum of Hydrogen to be “excited”. To produce an emission When an electric discharge is passed through spectrum, energy is supplied to a sample by gaseous hydrogen, the H2 molecules dissociate heating it or irradiating it and the wavelength and the energetically excited hydrogen atoms (or frequency) of the radiation emitted, as produced emit electromagnetic radiation of the sample gives up the absorbed energy, is discrete frequencies. The hydrogen spectrum recorded. consists of several series of lines named after An absorption spectrum is like the their discoverers. Balmer showed in 1885 photographic negative of an emission on the basis of experimental observations * The restriction of any property to discrete values is called quantization. 2024-25 Unit 2.indd 44 9/9/2022 4:28:11 PM  structure of atom 45 (a) (b) Fig. 2.10 (a) Atomic emission. The light emitted by a sample of excited hydrogen atoms (or any other element) can be passed through a prism and separated into certain discrete wavelengths. Thus an emission spectrum, which is a photographic recording of the separated wavelengths is called as line spectrum. Any sample of reasonable size contains an enormous number of atoms. Although a single atom can be in only one excited state at a time, the collection of atoms contains all possible excited states. The light emitted as these atoms fall to lower energy states is responsible for the spectrum. (b) Atomic absorption. When white light is passed through unexcited atomic hydrogen and then through a slit and prism, the transmitted light is lacking in intensity at the same wavelengths as are emitted in (a) The recorded absorption spectrum is also a line spectrum and the photographic negative of the emission spectrum. that if spectral lines are expressed in terms The value 109,677 cm –1 is called the of wavenumber ( ), then the visible lines of Rydberg constant for hydrogen. The first five the hydrogen spectrum obey the following series of lines that correspond to n1 = 1, 2, 3, formula: 4, 5 are known as Lyman, Balmer, Paschen, Bracket and Pfund series, respectively, (2.8) Table 2.3 shows these series of transitions in where n is an integer equal to or greater than the hydrogen spectrum. Fig. 2.11 (page, 46) 3 (i.e., n = 3,4,5,....) shows the Lyman, Balmer and Paschen series of transitions for hydrogen atom. The series of lines described by this formula Of all the elements, hydrogen atom has are called the Balmer series. The Balmer the simplest line spectrum. Line spectrum series of lines are the only lines in the hydrogen spectrum which appear in the visible region of the electromagnetic spectrum. The Swedish Table 2.3 The Spectral Lines for Atomic spectroscopist, Johannes Rydberg, noted Hydrogen that all series of lines in the hydrogen Series n1 n2 Spectral Region spectrum could be described by the following expression : Lyman 1 2,3.... Ultraviolet (2.9) Balmer 2 3,4.... Visible Paschen 3 4,5.... Infrared where n1=1,2........ Brackett 4 5,6.... Infrared n2 = n1 + 1, n1 + 2...... Pfund 5 6,7.... Infrared 2024-25 Unit 2.indd 45 9/9/2022 4:28:12 PM  46 chemistry atomic structure and spectra. Bohr’s model for hydrogen atom is based on the following postulates: i) The electron in the hydrogen atom can move around the nucleus in a circular path of fixed radius and energy. These paths are called orbits, stationary states or allowed energy states. These orbits are arranged concentrically around the nucleus. ii) The energy of an electron in the orbit does not change with time. However, the electron will move from a lower stationary state to a higher stationary state when required amount of energy is absorbed by the electron or energy is emitted when electron moves from higher stationary state to lower stationary state (equation 2.16). The energy change does not take place in a continuous manner. Angular Momentum Fig. 2.11 Transitions of the electron in the Just as linear momentum is the product hydrogen atom (The diagram shows the of mass (m) and linear velocity (v), angular Lyman, Balmer and Paschen series of momentum is the product of moment of transitions) inertia (I) and angular velocity (ω). For an electron of mass me, moving in a circular becomes more and more complex for heavier path of radius r around the nucleus, atom. There are, however, certain features angular momentum = I × ω which are common to all line spectra, i.e., Since I = mer2, and ω = v/r where v is the (i) line spectrum of element is unique and linear velocity, (ii) there is regularity in the line spectrum of ∴angular momentum = mer2 × v/r = mevr each element. The questions which arise are: What are the reasons for these similarities? Is it something to do with the electronic iii) The frequency of radiation absorbed or emitted when transition occurs between structure of atoms? These are the questions two stationary states that differ in need to be answered. We shall find later that energy by ∆E, is given by: the answers to these questions provide the key in understanding electronic structure of (2.10) these elements. Where E1 and E2 are the energies of the 2.4 Bohr’s Model for Hydrogen lower and higher allowed energy states Atom respectively. This expression is commonly Neils Bohr (1913) was the first to explain known as Bohr’s frequency rule. quantitatively the general features of the iv) The angular momentum of an electron structure of hydrogen atom and its spectrum. is quantised. In a given stationary state He used Planck’s concept of quantisation it can be expressed as in equation (2.11) of energy. Though the theory is not the modern quantum mechanics, it can still h m e v r  n. n = 1,2,3..... (2.11) be used to