In hydrogen spectrum, the shortest wavelength in the Balmer series is . The shortest wavelength in the Bracket series is [2023]

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Solution

Q.
In hydrogen spectrum, the shortest wavelength in the Balmer series is $λ$ . The shortest wavelength in the Bracket series is [2023]

1 $9 λ$

2 $16 λ$

3 $2 λ$

4 $4 λ$

Ans.
(4)

Shortest wavelength in Balmer series when transition of electron from $\infty$ to $n = 2$

$\frac{1}{λ} = R (\frac{1}{2^{2}} - \frac{1}{\infty^{2}})$

$\frac{1}{λ} = \frac{R}{2^{2}} = \frac{R}{4}$ ...(i)

For Brackett series,

$\frac{1}{λ'} = R {(1)}^{2} (\frac{1}{4^{2}} - \frac{1}{\infty^{2}}) = R (\frac{1}{4^{2}}) = \frac{R}{16}$ ...(ii)

Divide (i) by (ii), we get

$\frac{λ'}{λ} = \frac{16}{4} = 4 \Rightarrow λ' = 4 λ$

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