Dual Nature of Matter

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141 of 200

Question 141 of 200

Two streams of photons, possessing energies to five and ten times the work function of metal are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectron emitted, in the two cases respectively, will be

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Answer: (C) 2:32:3

Using Einstein's photoelectric equation,
Maximum kinetic energy, KEmax=E−ϕK{E}_{max}=E-\phi, where, EE is energy of photon and ϕ\phi is work function.
For two cases,
12mv12=5ϕ−ϕ=4ϕ\dfrac{1}{2}m{v}_{1}^{2}=5\phi -\phi =4\phi and 12mv22=10ϕ−ϕ=9ϕ\dfrac{1}{2}m{v}_{2}^{2}=10\phi -\phi =9\phi
Thus, the ratio v1v2=49=23=2:3\dfrac{{v}_{1}}{{v}_{2}}=\dfrac{4}{9}=\dfrac{2}{3}=2:3

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