Dual Nature of Matter & Radiation notes PDF

Okay here is the structured markdown format for the given document: # PHYSICS SCIENCE CAREER COACHING A Complete Science Solution Hub... ## Table of Contents | S.N. | TOPIC | Page No. | |-----|--------------------------------------------------...

Okay here is the structured markdown format for the given document: # PHYSICS SCIENCE CAREER COACHING A Complete Science Solution Hub... ## Table of Contents | S.N. | TOPIC | Page No. | |-----|-------------------------------------------------------------|----------| | 1. | Introduction | 01 | | 2. | Electron Emission | 02 | | 3. | Photoelectric Effect | 04 | | 4. | Important Graphs | 05 | | 5. | Law of Photoelectric Emission | 09 | | 6. | Einstein's Photoelectric Equation | 11 | | 7. | Important Graphs of Photoelectric Effect | 15 | | 8. | Particle Nature of Light | 17 | | 9. | Failure of Wave Theory of Light to Explain Photoelectric Effect | 18 | | 10. | Dual Nature of Radiations | 19 | | 11. | De-Broglie Dualistic Hypothesis | 20 | | 12. | De-Broglie Wavelength of Electron | 26 | | 13. | Experimental Demonstration of Wave Nature of Electron | 26 | | 14. | Very Important Questions | | ## 11. Dual Nature of Radiation & Matter ### Introduction The discovery of phenomena like interference, diffraction, and polarization of light established that light has a wave nature. Maxwell's equations of electromagnetism and Hertz's experiment on the production and detection of electromagnetic waves in 1886 strongly supported the concept of light's wave nature. In the 20th century, the discoveries of the photoelectric effect by Hertz and the Compton effect were explained by the quantum theory of light. According to quantum theory, light consists of packets of energy called photons (hv) that travel in a straight line with the speed of light. This established light's particle nature. ### Free Electrons In metals, electrons in the outer shells (valence electrons) of the atoms are loosely bound. They can move easily within the metal surface but cannot leave it. Such loosely bound electrons are called free electrons and are held inside the metal by the attractive force of the surface, called restraining forces. ### Work Function ($\Phi$) The work function of a metal is the minimum energy required for an electron to just escape from the metal surface, so as to overcome the restraining forces at the surface. It is represented by $\Phi$ and measured in eV. ### Electron Emission #### (i) Thermionic Emission This is the emission of electrons from the metal surface when heated suitably. The energy required for the emission of electrons from the metal surface is supplied by thermal energy. The emitted electrons are called thermal electrons or thermions. The number of thermions emitted depends on the temperature of the metal surface. Below is a description of the image in the document. Thermions are being emitted out of the metal slab that thermal energy is applied to. #### (ii) Secondary Emission This is the emission of electrons from the surface of a metal in large numbers when fast-moving electrons (primary electrons) strike the metal surface. The fast-moving electrons are high energy electrons. As they fall on the metal surface, they transfer their energy to the free electrons of the metal. Below is a description of the image in the document. A metal slab is being bombarded by primary electrons, which are causing secondary electrons to be emitted from the metal. ### Photoelectric Emission This is the phenomena of emission of electrons from the surface of a metal when light radiation of suitable frequency falls on it. The energy for emission is supplied by light photons, and the emitted electrons are called photoelectrons. The number of photoelectrons emitted depends on the intensity of the incident light. Below is a description of the image in the document. Photons are bombarding a metal slab, which is causing photoelectrons to be emitted from the metal. ### (iv) Field Emission/ Cold Cathode Emission This is the phenomena of emission of electrons form the metal surface under the application of a string electric field. When a very Strong electric Field ($10^8Vm^{-1}$)is applied to metal, it emits electrons. ### Photoelectric Effect The emission of electrons from the surface of metals, when radiation of suitable frequency fall on them.The emitted electrons are called photo-electrons and the current so produced is called photoelectric current. ### Experimental Study of Photoelectric Effect The apparatus consists of an evacuated glass or quartz tube which encloses a photosensitive plate C (called emitter) and metal plate A (called collector). A transparent window $W$ is sealed on the glass tube which can be covered with a filter for light of particular radiation. This will allow light of a particular wave length to pass through it. The plate A can be given a desired positive or negative potential with respect to plate C using the arrangement as shown in figure. The diagram shows an ammeter connected to the plate A and plate C via reversing key controlled by a battery. The transparent window is facing plate C. ### Working When monochromatic radiations of suitable frequency from source $S$, fall on photosensitive plate $C$, the photoelectrons are emitted from $C$, which get accelerated towards the plate $A$(collector) if it is kept at positive potentail. These electrons flow in in the outer circuit resulting in the photoelectric current. Due to it, the microammeter shows a deflection. The reading of microammeter measures the photoelectric current. This experimental arrangement can be used to study the variation of photoelectric current with the following quantities. #### (i) Effect of Intensity of the incident radiation. By varying the intensity of the incident radiations, keeping the frequency constant, it is found that the photoelectric current varies linearly with the intensity of the incident radiation. The plot shows Photoelectric Current and intensity as a linear plot. Also the number of photoelectrons emitted per second is directly proportional to the intensity of the incident radiations. #### (ii) Effect of potential of plate A w.r.t. plate $C$ It is found that the photoelectric current increases gradually with the increase in positive potential of plate A. At one stage for a certain positive potential of Plate A, the photoelectric current becomes maximum or saturates. After this if we increase the positive potential of plate A, there will be no increase in the photoelectric current. This maximum value of current is called saturation current. The saturation current corresponds to the state when all the photoelectrons emitted $C$ reach the plate $A$. The plot shows Photoelectric Current versus Potential for intensities $I_1, I_2, I_3$ where $I_3>I_2>I_1$ Now apply a negeative potential on plate $A$ w.r.t plate $C$. We will note that the photoelectric current decreases, because the photoelectrons emitted from $C$ are repelled and only energetic photoelectrons are reaching the plate $A$. By increasing the negative potential of plate $A$, the photoelectric current decreases rapidly and becomes zero at a certain value of negative potential $V_0$ on plate $A$. This maximum negative potential $V_0$, given to the plate $A$ w.r.t plate $C$ at which the photoelectric current becomes zero, is called stopping potential or cut off potential $K_{max} = eV_0 = \frac{1}{2}mv_{max}^2$ Where $e = charge$ on electron, $m= mass$ of electron $v_{max} = maximum$ velocity of emitted photoelectron. #### (iii) Effect of frequency of the incident radiation The value of the stopping potential is independent of the intensity of incident radiation. The stopping potential is more negative for radiation of higher incident frequency. The value of saturation current depends on the intensity of incident radiation, but is independent of the frequency of the incident radiation. The plot shows the photoelectric current versus the potential for frequencies $v_1, v_2, v_3$ where $v_3>v_2>v_1$. #### (iv) Effect of frequency on stopping potential For a given photosensitive material, the stopping potential varies linearly with the frequency of the incident radiation. For every photosensitive material, there is a certain minimum cut off frequency $v_0$ (Threshold frequency) for which the stopping potential is zero. The plot shows stopping potential versus frequency as a linear plot with the x-intercept marked as $v_0$. ### Note It is found that, if the incident radiation is of higher frequency than that of threshold frequency for which the emission of photoelectron is just possible, the photoelectric emission starts instantaneously, even if the incident light is very dim. The time lag between the incidence of radiation and emission of photoelectrons is less than $10^{-9}$ sec. ### Laws of Photo-Electric Emission 1. For a given metal and frequency of incident radiation, the number of photoelectrons ejected per second is directly proportional to the intensity of the incident light. 2. For a given metal, there exists a certain minimum frequency of the incident radiation below which no emission of photocurrents takes place. This frequency is called threshold frequency. 3. Above the threshold frequency, the maximum Kinetic energy of the emitted photoelectron is independent of the intensity of the incident hight but depends only upon the frequency of incident hight. 4. The photoelectron emission is an instantaneous process...The time lag betweent the incidence of radiations and emission of photoelectrons is very small , less than even $10^-9$ second. *Example Problem: The stopping potential in an experiment on photo- electric effect is 2v. What is the maximum Kinetic energy of the photoelectrons emitted?* Solution: Given that $V_o$ = 2V so Maximum Kinetic Energy $K_{max}$=$e$ $V_o$= $e$ x 2 = 2 $e$V *Example Problem : Show graphically how the maximum kinetic energy of electrons emitted from a photosensitive Surface varies with the frequency of incident radiations ?* The plot is a linear graph with the x-intercept marking frequency. The graph shows data for $Metal$ $A$ and $Metal$ $B$ with both having different slopes. ### Einstein's Photoelectric Equation According to Planck's quantum theory, light radiations consist of tiny packets of energy called quanta. One quantum of light radiation is called a photon which travels with the speed of light. $E = h \nu$ where h is plank's Constant and $\nu$ is the frequency of light radiation. Einstein assumed that one photoelectron is ejected from a metal surface if one photon of suitable light radiation falls on it. When a photon of light of frequency $\nu$, incident on a photosensitive metal surface, the energy of the photon ($h \nu$) is spent in tow ways: * A part of photon energy is used to free the electron from the metal surface which is equal to the work function ($\Phi_o$) of the metal * The rest of the energy of the photon is used in giving the maximum Kinetic energy $K_{max}$ to the emitted photoelectron. Max. Kinetic Energy of photoelectron $K_{max}=\frac{1}{2}mV^2$ $hv=\Phi_o + \frac {1}{2}mV^2$ $k_{max}=\frac{1}{2}mV^2=h\nu-\Phi$. This equation is called Einstein's photoelectric equation Also $ \Phi_o = h \nu$ where $\nu$ is threshold frequency. So that we can also write $K_{max}=h(\nu-v_o)$. ### Relation between Cut off Potential, Frequency of incident photon and Threshold Frequency. By Einstein's photoelectric equation - Max. Kinetic Energy $K = hv-\Phi_o$ If $V_o$ is the cut off potential or stopping potential and e. is is the charge. on the electron, then $K=eV_o$ It $v_o$ is the threshold frequency then. Work function $=hv_o$ so by combining equation (1), (2) and (3), we get - $eV_o=h(v-v_0)$. $eV_0=K=h(\frac{c}{2} - \frac{v}{i_o} )$. Or $eV_0=K = h c(\frac{1}{X} - \frac{1}{L_o} )$. ### Particle Nature of Light (The Photon) 1. In interaction of radiation with matter, radiation behaves as it is made of particles like photons. 2. Each photon has energy $E = h \nu=h_c/\lambda$ and momentum $ P = h\nu/ c=h \lambda$) 3. Irrespective of the intensity of radiation, all the photon's of a particular frequency 12. or wavelength $\lambda$ have the same energy $E = h \nun$ and the same momentum. 4. By increasing the intensity of radiation of a given frequency or wavelength on a metal surface, there is only increase in the number of photons persecond falling, on that surface, while each photon is having, the same energy. 5. All the photons emitted from a source of light travel through space with, the same speed which is equal to the speed of light. 6. The frequency of photon which shows a definite energy (or color), does notchange when photon travels through different media. 7. The velocity of photon in different media is different Which is due to change in its wavelength. 8. Photons are not deflected by electric and magnetic fields. Hence photons are electrically neutral **[Q]** **Radiations of** **frequency $10^{15} H_\mathbb{Z}$ are incident on two photosensitive surfaces A and B. Following observations are recorded.** * Surface A - No photo-electric emission take place * Burface 13 ~ Photo emission takes place but photoelectrons have zeroenergy Explain the above observations on the basis of Einstein's photo_electric equation, How will the observation with surface $B$ change when the *wavelength of incident radiations is decreased? **Sol: ** Einslein's Photoelectric equation states that = $K=h(v -v_o)$ For Surface $A_\mathbb{Z}$ no photoemission takes prace from surface $A$, it means $v$. **- De BROGLIE Wavelength of an Electron** - Consider an electron of mass m and charge e, $v$ be be the velocity acquired by elctrom when accelarated from rest though, a potential defference of $V$ volt. **Kinetic Energy of Electron** = = $\tfrac{1}{2} mV^2$ **"Work done on the electron = $v$ =eV.** $\frac{1}{2} mV^2$= eV or $V= \frac{1/2 eV }{n}$ if $A$ is me de-broglie wave length associated with mel * By substileting me Valnes of and ne $ger=$ λ= The wave nature of moving electrons has been established cxperimentally by Davisson and Germer in 1927 **Apparatus** - The apparatus consist of a filament of tungesten coated with berium oxide, which on heating with current from. low tension battery emits large numner of electronics * * C is a hollow metallic cylinder with a hole along The axis, it surrounds the filament and is kept al- negative potential, 50 that, the electrons emitted from filament May form a Convergent Deam of electrons. 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The mcidol exctons are scattered an alferent orections by one atom’s of one crystal.* " The mtensity of electron weam Scattered ing at given direction is found Oy me vse of dekxktr: Ny rotating me exctwon alekxikr On Ciralar Scale al- alfferent position's, the mtensoty of mo Scattered veam as measured for alforn* Here for me scaleerring angle 250°~, me angle of the exctron beam will be gwen yy & + ¢ + B = 980° Or QL iM80- $3 20, or The nehel crysral. 41 me mternatumic separation Ds~ a = aal. Q. $According to Bragg's Law for first oroler oliffraction ### Very Impotant Questions 1. Mark Questions - Q.1. Define the lern stopping polanttal relahon to phorvelerinc elfect- (CBSE2015. Show the variation of phorocurrent with collect. plate polontlal for dilgerenl Preqvencles. gut same intensity of mcidenl- radlation - CBSE206) Q.3 Show the variation of protocurrent with CoMleet. Plate polanttal fov dilferent intensmes. gut same Preqvenly 4 mcudenl- radratron- Q.4 The gtopping potential mn am experiment On photoelect-ric effect is is v. Wnal is me maximum Kinellc energy of Me protoelectrons ernitted 2 Answier = is ev CBSE206) Q.S The maximum Kinetic energy of a plooroelectron as Nev; mat is he gtopping "polonial.2 Answer = 2V @8Se 2o0d) Snou grophically how the stopping potential lor a given phorosensihive Surface varies with preqvenly of incvdert- radrations Q-F &lale de roglie ypamesis The information provided is a great start! The document appears to be an outline or set of notes on Physics, specifically focusing on wave-particle duality, the photoelectric effect, and related concepts. Would you like me to continue generating sections? The more information you give me, the more I can create the document for you in structured in markdown.