Question

A hydrogen atom, at rest, emits the β –line of its Balmer series. The recoil energy of the hydrogen atom, in terms of R (= Rydberg’s constant for hydrogen), h (= Planck’s constant) and M (= Mass of hydrogen atom), would be

Answer 1

Correct option : (2)

Explanation:

The β –line, in the Balmer series, corresponds to a transition from n₂ = 4 to n₁ = 2. The wavelength, λ, of this β –line, is given by

The linear momentum of the emitted photon 

The hydrogen atom is initially at rest. To conserve linear momentum, the recoil momentum of the hydrogen atom, is also p, directed in a direction opposite to the direction of motion of the photon. Hence the recoil energy of the hydrogen atom