The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is [2007]

Question

The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is [2007]

Smart Achievers · Accepted Answer

(2)

The smallest frequency and longest wavelength in the ultraviolet region will be for transition of electron from $n = 2$ to $n = 1$ , i.e., Lyman series.

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

$\Rightarrow \frac{1}{122 \times 10^{- 9} m} = R (\frac{1}{1^{2}} - \frac{1}{2^{2}}) = R (1 - \frac{1}{4}) = \frac{3 R}{4}$

$∴$ $R = \frac{4}{3 \times 122 \times 10^{- 9}} m^{- 1}$

The highest frequency and smallest wavelength for the infrared region will be for transition of electron $n = \infty, n = 3$ corresponding to Paschen series.

$∴$ $\frac{1}{λ} = R (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$ $\Rightarrow \frac{1}{λ} = \frac{4}{3 \times 122 \times 10^{- 9}} (\frac{1}{3^{2}} - \frac{1}{\infty})$

$∴$ $λ = \frac{3 \times 122 \times 9 \times 10^{- 9}}{4} = 823.5 nm$

Solution

Q.
The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is [2007]

1 802 nm

2 823 nm

3 1882 nm

4 1648 nm

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