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JEE Main & Advanced Physics Photo Electric Effect, X- Rays & Matter Waves Question Bank Critical Thinking

  • question_answer
    In a photocell bichromatic light of wavelength 2475 Å and 6000 Å are incident on cathode whose work function is 4.8 eV. If a uniform magnetic field of 3 ´ 10?5 Tesla exists parallel to the plate, the radius of the path describe by the photoelectron will be (mass of electron = 9 ´ 10?31 kg)

    A)            1 cm                                         

    B)            5 cm

    C)            10 cm                                      

    D)            25 cm

    Correct Answer: B

    Solution :

                       Energy of photons corresponding to light of wave length l1 = 2475 Å is \[{{E}_{1}}=\frac{12375}{2475}=5\,eV.\]                    and that corresponding to l2 = 6000 Å is                    \[{{E}_{2}}=\frac{12375}{6000}=2.06\,eV\]                    As E2 < W0 and E1 > W­0                    Photoelectric emission is possible with l1 only. Maximum kinetic energy of emitted photoelectrons K = E ? W0 = 5 ? 4.8 = 0.2 eV.                    Photo electrons experiences magnetic force and move along a circular path of radius                    \[r=\frac{\sqrt{2\,mk}}{Q\,B}=\frac{\sqrt{2\times 9\times {{10}^{-31}}\times 0.2\times 1.6\times {{10}^{-19}}}}{1.6\times {{10}^{-19}}\times 3\times {{10}^{-5}}}\]                    = 0.05 m = 5 cm.


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