A) \[5\times {{10}^{11}}\]
B) \[2.5\times {{10}^{11}}\]
C) \[3\times {{10}^{11}}\]
D) none of these
Correct Answer: B
Solution :
From Einsteins photoelectric effect concept the energy of these photons, for light of frequency v is \[E=hv\] where h is Plancks constant. Also frequency \[=\frac{velocity}{wavelength}=\frac{c}{\lambda }\] \[=\frac{hc}{\lambda }\] Energy of n photons is \[E=\frac{nhc}{\lambda }\] Given, \[E={{10}^{-7}}\,J,\,\lambda =5000\,\overset{o}{\mathop{A}}\,\] \[=5000\times {{10}^{-10}}m\] \[\Rightarrow \] \[n=\frac{E\lambda }{hc}\] \[=\frac{{{10}^{-7}}\times 5000\times {{10}^{-10}}}{6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}}\] \[=2.5\times {{10}^{11}}\]
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