Question

Calculate the ratio of frequencies of the radiation emitted due to transition of electron in hydrogen atom from its second permitted energy level to first level and highest permitted energy level to the second permitted level

Answer 1

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Answer 2

The ratio of frequencies of the radiation emitted due to the transition of an electron in a hydrogen atom from its second permitted energy level to the first level and highest permitted energy level to the second permitted level = 3

Given,

E₂₋₁ = Transition of an electron from the second permitted energy level to the first level

E∞₋₂ = Transition of an electron from the highest permitted energy level to the second permitted level

To Find,

The ratio of frequencies of the radiation emitted due to the transition of an electron in a hydrogen atom from its second permitted energy level to the first level and highest permitted energy level to the second permitted level = E₂₋₁/E∞₋₂

Solution,

The emission range of nuclear hydrogen has been isolated into various spectral series, with frequencies given by Rydberg's formula. These noticed spectral lines are because of the electron-making changes between two energy levels in a particle.

The energy of an electron in the nth energy level is given by -

Eₙ = $\frac{-13.6}{n^2}$ eV

E₂₋₁ = $\frac{-13.6}{2^2} - \frac{-13.6}{1^2}$

E₂₋₁ = $\frac{-13.6}{4} - \frac{-13.6}{1}$

E₂₋₁ = - 3.4 + 13.6

E₂₋₁ = 10.2 eV

E∞₋₂ = $\frac{-13.6}{(infinity)^2} - \frac{-13.6}{2^2}$

E∞₋₂ = $0 - \frac{-13.6}{4}$

E∞₋₂ = 3.4 eV

Thus, the ratio is -

E₂₋₁/E∞₋₂ = 10.2/3.4

E₂₋₁/E∞₋₂ = 3

Hence, the required ratio is 3.

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