(2) \(\frac{9h^2R^2}{512M}\)
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 = p = h/λ or p = 3hR/16
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