When a photon is emitted by a hydrogen atom, it carries momentum. A hydrogen atom emits light of wavelength 656.3 nm . Determine the speed at which the atom recoils during this transition. Take the mass of the hydrogen atom to be 1.67 10⁻²⁷ kg .

Step-by-step solution

By the principle of conservation of momentum, the recoil momentum of the hydrogen atom is equal in magnitude to the momentum of the emitted photon. p_ atom = p_ photon m v = h v = h m Substituting the given values, with h = 6.63 10⁻³⁴ J s : v = 6.63 10⁻³⁴ 1.67 10⁻²⁷ 656.3 10⁻⁹ v = 6.63 10⁻³⁴ 1096.02 10⁻³⁶ v = 6.63 10.96 0.6 m s ⁻¹