A) \[4.718\text{ }m{{s}^{-1}}\]
B) \[7.418\text{ }m{{s}^{-1}}\]
C) \[4.178\text{ }m{{s}^{-1}}\]
D) \[7.148\text{ }m{{s}^{-1}}\]
Correct Answer: C
Solution :
\[E={{R}_{\infty }}hc\left[ 1-\frac{1}{25} \right]\] Momentum of photon emitted is \[P=\frac{E}{c}={{R}_{\infty }}h\left[ \frac{24}{25} \right]\] Recoil momentum of H-atom will also be p \[\Rightarrow \] \[mv=p\] \[\Rightarrow \]\[v=\frac{p}{m}=\frac{(1.097\times {{10}^{7}})(6.626\times {{10}^{-34}})24}{(25)(1.67\times {{10}^{-27}})}\] \[\Rightarrow \] \[v=4.178\,m{{s}^{-1}}\]
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