Find the temperature at which the average thermal kinetic energy is equal to the energy needed to take a hydrogen atom from its ground state to n = 3 state. Hydrogen can now emit red light of wavelength 653.1 nm. Because of Maxwellian distribution of speeds, a hydrogen sample emits red light at temperatures much lower than that obtained from this problem. Assume that hydrogen molecules dissociate into atoms.
K = 8.62 x10–5 eV/k
K.E. of H2 molecules = 3/2 KT
Energy released, when atom goes from ground state to no = 3
=>13.6 (1/1 – 1/9) => 3/2 KT = 13.6(1/1 – 1/9)
=> 3/2 x 8.62 x 10-5 T=13.6 x 8/9
=>T=0.9349 x 105=9.349 x 104=9.4 x 104K.
