First slide

Hydrogen spectrum

Question

If the series limit of Lymen series for Hydrogen atom is equal to the series limit of Balmer series for a hydrogen like atom, then atomic number of this hydrogen-like atom
will be

Moderate

A

1
B

2
C

3
D

4

Solution

$By using \frac{1}{λ} = R Z^{2} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] For hydrogen atom, \frac{1}{{(λ_{min})}_{H}} = R [\frac{1}{1^{2}} - \frac{1}{\infty}] = R \Rightarrow {(λ_{min})}_{H} = \frac{1}{R} . . . . . . . (i) For hydrogen like atom {(\frac{1}{λ_{min}})}_{atom} = R Z^{2} (\frac{1}{2^{2}} - \frac{1}{\infty}) \Rightarrow {(λ_{min})}_{atom} = \frac{4}{R Z^{2}} . . . . . . . . . . (i i) From equations (i) and (ii), \frac{1}{R} = \frac{4}{R Z^{2}} \Rightarrow Z = 2$

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