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 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) |
| or \[\frac{1}{2}m\times {{v}^{2}}=5h{{v}_{0}}-h{{v}_{0}}\] (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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