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Q)

What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition n=4 to n=2 of $He^+$ spectrum ?

$(a)\;2,3\qquad(b)\;3,1\qquad(c)\;3,2\qquad(d)\;1,2$

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A)
For $He^+,\large\frac{1}{\lambda}$$=R_Hz^2\bigg[\large\frac{1}{2^2}-\frac{1}{4^2}\bigg]$
For $H,\large\frac{1}{\lambda}$$=R_H\bigg[\large\frac{1}{n_1^2}-\frac{1}{n_2^2}\bigg]$
Since $\lambda$ is same
$\therefore Z^2\bigg[\large\frac{1}{2^2}-\frac{1}{4^2}\bigg]=\bigg[\large\frac{1}{n_1^2}-\frac{1}{n_2^2}\bigg]$
$z=2$
$\bigg[\large\frac{1}{1^2}-\frac{1}{2^2}\bigg]=\bigg[\large\frac{1}{n_1^2}-\frac{1}{n_2^2}\bigg]$
$n_1=1$ and $n_2=2$
Hence (d) is the correct answer.
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