What is the wavelength of the light emitted when an electron in a hydrogen atom undergoes transition from the energy level n = 4 to energy level n = 2? What is the colour corresponding to their wavelengths? (Given $R_{H} = 109677 c m^{- 1}$ )

486 nm, Blue

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576 nm, Blue

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650, Blue

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450 nm, Blue

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Solution

The correct option is A
486 nm, Blue

According to Balmer equation,
Wave number $(¯ ν) = R_{H} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}] c m^{- 1}$
$n_{1} = 2, n_{2} = 4, R_{H} = 109677 c m^{- 1}$
Substituting all the values, we get
$¯ ν = 109677 [\frac{1}{(2)^{2}} - \frac{1}{(4)^{2}}] c m^{- 1} = \frac{109677 \times 3}{16} c m^{- 1}$
Or $λ = \frac{1}{¯ ν} = \frac{16}{109677 \times 3} c m = 486 n m$
The wavelength corresponds to blue color.

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What is the wavelength of the light emitted when an electron in a hydrogen atom undergoes transition from the energy level n = 4 to energy level n = 2? What is the colour corresponding to their wavelengths? (Given RH=109677 cm−1)

The correct option is A 486 nm, Blue According to Balmer equation, Wave number (¯ν)=RH[1n21−1n22]cm−1 n1=2, n2=4, RH=109677 cm−1 Substituting all the values, we get ¯ν=109677[1(2)2−1(4)2]cm−1=109677×316cm−1 Or λ=1¯ν=16109677×3cm=486 nm The wavelength corresponds to blue color.

What is the wavelength of the light emitted when an electron in a hydrogen atom undergoes transition from the energy level n = 4 to energy level n = 2? What is the colour corresponding to their wavelengths? (Given $R_{H} = 109677 c m^{- 1}$ )