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The Line Spectra of the Hydrogen Atom

The largest wavelength in the ultraviolet region of the hydrog

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The largest wavelength in the ultraviolet region of the hydrogen spectrum is $122 nm$ . The smallest wavelength (in $nm$ ) in the infrared region of the hydrogen spectrum is

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Updated on: Mar 31, 2023

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The largest wavelength in the ultraviolet region of the hydrogen spectrum is

122 nm

. The smallest wavelength (in

nm

) in the infrared region of the hydrogen spectrum is

5 mins ago

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Text solutionVerified

The smallest frequency and largest wavelength in ultraviolet region will be for transition of electron from orbit 2 to orbit

1.

∴ \frac{1}{λ} = R (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}})

\Rightarrow \frac{1}{122 \times 1 0 ^{- 9} m} = R [\frac{1}{1 ^{2}} - \frac{1}{2 ^{2}}] = R [1 - \frac{1}{4}] = \frac{3 R}{4}

\Rightarrow R = \frac{4}{3 \times 122 \times 1 0 ^{- 9}} m^{- 1}

The highest frequency and smallest wavelength for infrared region will be for transition of electron from

\infty

to 3 rd orbit.

∴ \frac{1}{λ} = R (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}}) \Rightarrow \frac{1}{λ} = \frac{4}{3 \times 122 \times 1 0 ^{- 9}} (\frac{1}{3 ^{2}} - \frac{1}{\infty})

∴ λ = \frac{3 \times 122 \times 9 \times 1 0 ^{- 9}}{4} = 823.5 nm

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Question Text	The largest wavelength in the ultraviolet region of the hydrogen spectrum is $122 nm$ . The smallest wavelength (in $nm$ ) in the infrared region of the hydrogen spectrum is
Updated On	Mar 31, 2023
Topic	Atoms
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 4
Upvotes	401
Avg. Video Duration	3 min

The largest wavelength in the ultraviolet region of the hydrogen spectrum is $122 nm$ . The smallest wavelength (in $nm$ ) in the infrared region of the hydrogen spectrum is

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The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength (in nm ) in the infrared region of the hydrogen spectrum is

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The largest wavelength in the ultraviolet region of the hydrogen spectrum is $122 nm$ . The smallest wavelength (in $nm$ ) in the infrared region of the hydrogen spectrum is