A) \[2\times {{10}^{6}}\,m/s\]
B) \[2\times {{10}^{7}}\,m/s\]
C) \[8\times {{10}^{5}}\,m/s\]
D) \[8\times {{10}^{6}}\,m/s\]
Correct Answer: D
Solution :
Key Idea: The solution to our problem consists in Einstein?s photoelectric equation. Einstein?s 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 \[\frac{{{v}^{2}}}{{{(4\times {{10}^{6}})}^{2}}}=\frac{4h{{v}_{0}}}{h{{v}_{0}}}\] \[\Rightarrow {{v}^{2}}=4\times 16\times {{10}^{12}}\] \[\Rightarrow {{v}^{2}}=64\times {{10}^{12}}\] \[\therefore v=8\times {{10}^{6}}\,m/s\] 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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