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An electron changes its position from orbit n = 2 to the orbit n = 4 of an atom. The wavelength of the emitted radiations is (R = Rydberg’s constant).

1. 16 / R
2. 16 / 3R
3. 16 / 5R
4. 16 / 7R

Correct answer: 16 / 7R

Solution

The wavelength of emitted radiation is calculated using the Rydberg formula: 1/λ = R(1/n₁² - 1/n₂²). Substituting n₁ = 2 and n₂ = 4, we get 1/λ = R(1/2² - 1/4²) = R(1/4 - 1/16) = R(4/16 - 1/16) = R(3/16). Thus, λ = 16/3R.

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