Question

The energy levels of a certain atom for first, second and third levels are E, 4E/3 and 2E, respectively. A photon of wavelength λ is emitted for a transition 3 `→` 1. What will be the wavelength of emission for transition 2 `→` 1?

Options

• `lambda/3`

• `(4lambda)/3`

• `(3lambda)/4`

• 3λ

Answer 1

3λ

Explanation:

E = `"ch"/lambda` or E∝ `1/lambda` or λE = constant

Given: E₁ = E, E₂ = `(4"E")/3`, E₃ = 2E   

E₃ – E₁ = 2E – E = E

wavelength of the emitted photon is

∴ E₂ - E₁ = `(4"E")/3-"E" = "E"/3`

λE = λ' `"E"/3`

λ' = 3λ