A) 1 : 1
B) 1 : 2
C) 1 : 4
D) 1 : 5
Correct Answer: B
Solution :
From Einsteins photoelectric equation, we get \[{{E}_{k}}=hv-W\] In first case \[\frac{1}{2}m{{v}^{2}}=1\,eV-0.5\,eV=0.5\,eV\] ... (i) In second case \[\frac{1}{2}mv_{1}^{2}=2.5\,eV-0.5\,eV=2\,eV\] ... (ii) Dividing Eqs. (ii) by (i), we get \[\frac{v_{1}^{2}}{{{v}^{2}}}=\frac{2}{0.5}=4\] \[\Rightarrow \] \[\frac{{{v}_{1}}}{v}=\frac{2}{1}\] \[\Rightarrow \] \[\frac{v}{{{v}_{1}}}=\frac{1}{2}\]
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