A) \[2\times {{10}^{6}}m\text{/}s\]
B) \[2\times {{10}^{7}}m\text{/}s\]
C) \[8\times {{10}^{5}}m\text{/}s\]
D) \[8\times {{10}^{6}}m\text{/}s\]
Correct Answer: D
Solution :
Key Idea: The solution to our problem consists, in Einsteins photoelectric equation. Einsteins photoelectric equation can be written as \[\frac{1}{2}m{{v}^{2}}=hv-\phi \] \[\Rightarrow \] \[\frac{1}{2}m\times {{(4\times {{10}^{6}})}^{2}}=2h{{v}_{0}}-h{{v}_{0}}\] ?(i) and \[\frac{1}{2}m\times {{v}^{2}}=5h{{v}_{0}}-h{{v}_{0}}\] ?(ii) Dividing Eq. (ii) by (i), we get \[\frac{{{v}^{2}}}{{{(4\times {{10}^{6}})}^{2}}}=\frac{4h{{v}_{0}}}{h{{v}_{0}}}\] \[\Rightarrow \] \[{{v}^{2}}=4\times 16\times {{10}^{12}}\] \[\Rightarrow \] \[{{v}^{2}}=64\times {{10}^{12}}\] \[\therefore \] \[v=8\times {{10}^{6}}\,m\text{/}s\] NOTE: The efficiency of photoelectric effect is less than 1% i.e., number of photons less than 1% are capable of ejecting photoelectrons.
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