What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from an energy level with $n = 4$ to $n = 2$ ?

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Solution

$E = 2.18 \times 10^{- 18} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]$

$= 2.18 \times 10^{- 18} [\frac{1}{16} - \frac{1}{4}]$

$E = - (4.0875 \times 10^{- 19} J)$

negative sign indicates energy emission

$λ = \frac{h c}{E}$

$λ = \frac{(6.625 \times 10^{- 34}) \times (3 \times 10^{8})}{4.0875 \times 10^{- 19}}$

$λ = 486 n m$

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Q. What is the wavelength of light emitted when the electron in a hydrogen atom undergoes a transition from n = 4 to n = 2?

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What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from an energy level with n=4 to n=2?

E=2.18×10−18[1n21−1n22]=2.18×10−18[116−14]E=−(4.0875×10−19J)negative sign indicates energy emissionλ=hcEλ=(6.625×10−34)×(3×108)4.0875×10−19λ=486nm

What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from an energy level with $n = 4$ to $n = 2$ ?