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Two radiations of photons energies 1 eV and 2.5 eV, successively illuminate a photosensitive metallic surface of work function 0.5 eV. The ratio of the maximum speeds of the emitted electrons is
A
1 : 5
B
1 : 4
C
1 : 2
D
1 : 1
Detailed Solution
Einstein's equation: $\frac{1}{2}mv_{max}^2 = h\nu - W$
$\frac{(v_1)_{max}}{(v_2)_{max}} = \sqrt{\frac{h\nu_1 - W}{h\nu_2 - W}} = \sqrt{\frac{1 - 0.5}{2.5 - 0.5}}$
$= \sqrt{\frac{0.5}{2}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$
So the ratio is 1 : 2.
$\frac{(v_1)_{max}}{(v_2)_{max}} = \sqrt{\frac{h\nu_1 - W}{h\nu_2 - W}} = \sqrt{\frac{1 - 0.5}{2.5 - 0.5}}$
$= \sqrt{\frac{0.5}{2}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$
So the ratio is 1 : 2.