A) \[2.92\times {{10}^{6}}m/s\]
B) \[1.46\times {{10}^{6}}m/s\]
C) \[0.73\times {{10}^{6}}m/s\]
D) \[3.0\times {{10}^{8}}m/s\]
Correct Answer: B
Solution :
Energy of electron in the 3rd orbit of \[H{{e}^{+}}\] is \[{{E}_{3}}=-13.6\times \frac{{{Z}^{2}}}{{{n}^{2}}}eV=-13.6\times \frac{4}{{{3}^{2}}}eV\] \[=-13.6\times \frac{4}{9}\times 1.6\times {{10}^{-19}}J\] From Bohr's model, \[{{E}_{3}}=-K{{E}_{3}}=-\frac{1}{2}{{m}_{e}}{{v}^{2}}\] \[\Rightarrow \,\,\,\,\frac{1}{2}\times 9.1\times {{10}^{-31}}\times {{v}^{2}}\] \[=-13.6\times \frac{4}{9}\times 1.6\times {{10}^{-19}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,{{v}^{2}}=\frac{136\times 16\times 4\times 2\times {{10}^{-11}}}{9\times 91}\] or \[v=1.46\times {{10}^{6}}m/s\]
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