Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
An electron in hydrogen atom first jumps from second excited state to first excited state and then from first excited state to ground state. Let the ratio of wavelength, momentum and energy of photons emitted in these two cases be a, b and c respectively. Then (1) \[c=\frac{9}{4}\] (2) \[c=\frac{5}{27}\] (3) \[a=\frac{9}{4}\] (4) \[b=\frac{5}{27}\]A) 1, 2 and 3 are correct
B) 1 and 2 are correct
C) 2 and 4 are correct
D) 1 and 3 are correct
Correct Answer: C
Solution :
\[E\propto \frac{1}{\lambda }\]and \[p\propto E\] \[\left( E=\frac{hc}{\lambda },p=\frac{E}{c} \right)\] Further \[E\propto \frac{1}{{{n}^{2}}}\] \[\therefore \] \[b=c\]and \[a=\frac{1}{b}\] and \[c=\frac{1/{{2}^{2}}-1/{{3}^{2}}}{1-1/{{2}^{2}}}=\frac{5}{27}\] \[\therefore \] \[b=c=\frac{5}{27}\] and \[a=\frac{27}{5}\]
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