A) \[\frac{24Rh}{25m}\]
B) \[\frac{25hR}{24m}\]
C) \[\frac{25m}{24hR}\]
D) \[\frac{24m}{25hR}\]
Correct Answer: A
Solution :
\[\frac{1}{\lambda }=R\left[ \frac{1}{{{n}^{2}}_{f}}-\frac{1}{{{n}^{2}}_{1}} \right]\] \[{{n}_{f}}=1,\,\,\,{{n}_{1}}=5\] \[\frac{1}{\lambda }=R\left[ 1-\frac{1}{{{\left( 5 \right)}^{2}}} \right]=\frac{24}{25}R\] Apply momentum conservation Momentum of photon = momentum of atom \[\frac{\operatorname{h}}{\lambda }=mv\] \[\operatorname{v}=\frac{h}{m\lambda }=\frac{h}{m}\times \frac{24}{25}R\] \[\operatorname{v}=\frac{24hR}{25m}\]
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