A) \[\frac{24hR}{25m}\]
B) \[\frac{25hR}{24m}\]
C) \[\frac{25m}{24hR}\]
D) \[\frac{24m}{25hR}\]
Correct Answer: A
Solution :
[a] For emission, the wave number of the radiation is given as \[\frac{1}{\lambda }=R{{z}^{2}}\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)\] R= Rydberg constant, z = atomic number \[=R\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{5}^{2}}} \right)=R\left( 1-\frac{1}{25} \right)\] \[\Rightarrow \] \[\frac{1}{\lambda }=R\frac{24}{25}\] linear momentum \[P=\frac{h}{\lambda }=h\times R\times \frac{24}{25}\](de-Broghe hypofliesis) \[\Rightarrow \] \[mv=\frac{24hR}{25}\Rightarrow \,\,v=\frac{24hR}{25m}\]
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