✤ PHOTONS : These are the packets of energy.

                         Some terms related to photons:

                               1. Energy associated with a photon E=h𝜈 joules

                                     Here h = 6.6 x 10^-34 JxS.

                                      𝜈=frequency

                               2. speed of Photon is about 3x10^8 ms-1.

                               3. Photon can't be deflected by electric or magnetic field.

                               4. Photons always travel in straight path.

✤ Free electrons : In metals, electrons in outermost shell of atoms are loosely bound. Such loosely bound electron are called free electrons.

✤ Work function : It is defined as the minimum energy required by an electron to just escape from metal surface so as to overcome the restraining forces                                 at the surface.: W=h𝜈0

                                ❆ Here 𝜈0-threshold unit is joule frequency. or ev

                                                    ev = 1.6 x 10-19 J.

✤ Electron emission: The phenomenon of emission of electron from the surface of metal is called electron emission.

✤ Photoelectric emission: It is the phenomenon of emission of electron from the surface of metals, when radiations of suitable frequency fall on them.

                                        Ex - Alkali metals

✤ Threshold frequency: It is the minimum freq. of incident radiations of required to emit the electrons from emitter.

                                           § at threshold freq. k. E of electron = 0

✤ Effect of intensity on photo electric current:

                          Current α intensity

                                     (no of energy quanta per unit area per unit time )

✤ Effect of Potential on current:

                      at stopping Potential

                              Kman = eVo

                                        = ½mv²

✤ No. of electrons ejected from metal surface

               For a particular frequency of incident radiation the minimum(-ve) retarding potential                Vo given to plate for which the photoelectric current become

               zero is called Stopping potential.

    Effect of frequency

        1. The value of stopping potential is different for different frequency.

              Stopping potential is independent of Intensity.

        2. More frequency, more stopping Potential.

        3. The value of saturated current depend upon intensity of light. Intensity α 1/(Distance)²

                    1. For a given metal plate, stopping Potential α frequency

                                

                    2. at threshold frequency

                              Vo = 0

                    3. higher the work function, greater frequency!

                    4. work function = ex magnitude of slope.

                        

✤ 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 intensity of

             incident radiation.

        2. For a given metal, there is a minimum freq. required below which emission of electrons does not take place, the freq. is called threshold

             frequency.

        3. K.E. of ejected photo electron does not depend upon the intensity. It depend upon the freq. of incident radiation.

        4. It is an instantaneous Process.

✤ EINSTEIN'S Equation

     When energy is supplied to a photosensitive plate then some part of energy is used as work function and remaining part is used to provide K.E.

                            i.e. hv = w + k.e

                                  hv = hv₀ + ½mv²

                                  h(v-v₀) = ½mv²

✤ De-Broglie hypothesis:

              →  According to de-broglie a moving material particle sometimes act as a wave and some time as a particle and the wave associated with particle                    control it in all respect. Wavelength of the wave

                                            λ = h/P

                             λ = h/mv Here p = momentum

                                          p = mv.

                                          p = mc.

                      de broglie's wave length associated with moving electron:

                              Since we know K.E = 1/2 mv² and K.E = eV.

                                                         → 1/2 mv² = eV

      v = √2eV/m

      λ = h/mv.

      λ = h/√2 mev

      λ = 12.27/√V A°

       1. Energy of a photon, E = hv

                  E = RC/λ

       2. no. of photons ejected per second ∝ N = P/E

       3. momentum of photon p = mc

                      p = h/λ

                      p = hv/c

  4. work function w = hv₀ = hc/λ₀

  5. K.E = 1/2 mv²max

                = eV₀, V₀ → stopping potential

  6. Einstein's Eq. h(v - v₀) = 1/2 mv²

  7. Intensity of radiation = Energy / (area × time) = Power / area.

                    ev = 1.6 x 10⁻¹⁹ J

                    h = 6.6 x 10⁻³⁴ JxS.

  8. K.E = p²/2m or momentum = √2mk

  9. debroglie wave length λ= h/p = h/√2mk

  10. wave length of wave associated with moving electron

                λ = 12.27 Å/√V → voltage

  11. wave length with temp

                λ ∝ 1/√T T is kelvin

Sol.  Different electrons belong to different energy levels in the conduction band. They need different energies to come out the metal surface for

          the same incident radiation.

2. How can you explain the emission of electron from metal by Einstein's Equation?

Sol. By Einstein's h = Wo + Kmax, when a photon of energy hv is incident on a metal, a part of this energy equal to work function Wo is used to

       removing the electron and remaining energy is used as K.E.

3.      (i) Metal A has higher work function and higher threshold frequency.

4. Draw a plot showing variation of Photo electric current with collector potential for two different frequency v1>v2. In which case stopping potential is     higher? Justify your Answer.

                          For v1 > v2

5. Plot a graph showing variation of de broglie wave length λ versus 1/√v, Here V is accelerating Potential for two         Particle A and B carrying same charge but masses m₁, m₂ (m₁>m₂)

Sol.    

                          ∴ Vp/Va = 8/1

        (ii) λ = h/mv

                       => Vp/Va = ma/mp = 4:1

7. The work function for following metals is given Na = 2.75 ev, k = 2.30 ev, Mo = 4.17ev, Ne: 5.15ev which of these metal will not emit Photo electron     for λ=3300Å from a He-Cd Laser which is 1 m away from the metal. What happened when laser bring close to metal plate.

    Sol. λ = 3300×10⁻¹⁰m

                      E= hc/λ = 3.75ev, so metal Na and k emit P.E. only.

                      (ii) If laser is bring close to plate then intensity of light increases so, number of photoelectron ↑.

8. Ultra voilet light of λ=2271 Å° from 100W laser on M0 metal surface. If stopping potential is 13 V. Estimate the work function. How would M₀ respond     to a high intensity (10⁵ Wm²) red light of wave length 6328 Å° produced by laser.

Sol. By Einstein's law hv-Wo= K.E

       hv-Wo = eVo

       Wo = hv-eVo

       Wo = 4.2 ev (solve yourself)

      and V0 = h/λ = 1.0 x 10¹⁵ Hz

      for λ = 6328 Å° = 6320 x 10⁻¹⁰ m.

       ∴ v = 4.74 x 10¹⁴ Hz.

                  Here v

9. The stopping potential is an experiment is 1.5 V. What is the maximum K.E.

Sol.      K.E = eVo

            = 1.6 x 10⁻¹⁹ x 1.5

              K.E = 1.5 ev.

10. If light of wave length 412.5 nm is incident on each of the metals, which ones will show photo-electric emission and why?

Sol.      E = hv/λ

               = 3.01 eV

          ∴ Sodium (Na) and Potassium (k)

          Shows photo electric effect.

11. If KE = 2 eV find stopping potential ? 

Sol.   eVo = 2eV Vo = 2V

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