When a photon is emitted by a hydrogen atom, it carries momentum. A hydrogen atom emits light of wavelength 656.3 nm . Find the kinetic energy of recoil of the atom. Take the mass of the hydrogen atom to be 1.67 10⁻²⁷ kg .

Step-by-step solution

The momentum of the emitted photon is given by p = h By conservation of linear momentum, the recoil momentum of the hydrogen atom is equal in magnitude to the momentum of the photon. The kinetic energy of recoil of the atom is K = p^2 2m = h^2 2m ^2 Substituting the given values: K = (6.63 10⁻³⁴)^2 2 1.67 10⁻²⁷ (656.3 10⁻⁹)^2 J K = 43.96 10⁻⁶⁸ 3.34 10⁻²⁷ 4.3 10⁻¹³ J 3.05 10⁻²⁸ J Converting the energy into electron-volts (eV): K = 3.05 10⁻²⁸ 1.6 10⁻¹⁹ eV 1.9 10⁻⁹ eV