A) 4
B) 1
C) 2
D) 3
Correct Answer: C
Solution :
Lyman series for H-ion \[\frac{hc}{\lambda }=Rhc\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right)\] and for H-like ion \[\frac{hc}{\lambda }={{Z}^{2}}Rhc\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{4}^{2}}} \right)\] \[\therefore \] \[\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right)={{Z}^{2}}\left( \frac{1}{4}-\frac{1}{16} \right)\] \[\left( 1-\frac{1}{4} \right)={{Z}^{2}}\left( \frac{1}{4}-\frac{1}{16} \right)\] \[Z=2\]
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