A) 1
B) 2
C) 3
D) 4
Correct Answer: B
Solution :
Let ground state energy (in eV) be \[{{E}_{1}}\] Then from the given condition \[{{E}_{2n}}-{{E}_{1}}=204\,eV\] or \[\frac{{{E}_{1}}}{4{{n}^{2}}}-{{E}_{1}}=204\,eV\] Þ \[{{E}_{1}}\left( \frac{1}{4{{n}^{2}}}-1 \right)=204\,eV\] ?..(i) and \[{{E}_{2n}}-{{E}_{n}}=40.8\,eV\] Þ \[\frac{{{E}_{1}}}{4{{n}^{2}}}-\frac{{{E}_{1}}}{{{n}^{2}}}={{E}_{1}}\left( -\frac{3}{4{{n}^{2}}} \right)=40.8\,eV\] ?..(ii) From equation (i) and (ii), \[\frac{1-\frac{1}{4{{n}^{2}}}}{\frac{3}{4{{n}^{2}}}}=5\] Þ \[n=2\]
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