Question

(a) By using the deBroglie relation, derive the Bohr condition mvr = nℏ for the angular momentum of an electron in a hydrogen atom.

(b) Use this expression to show that the allowed electron energy states in hydrogen atom can be written

(c) How would this expression be modified for the case of a triply ionized beryllium atom Be(Z = 4)?

(d) Calculate the ionization energy in eV of Be+3 (ionization energy of hydrogen = 13.6 eV)

Answer 1

(a) Stationary orbits will be such that the circumference of a circular orbit is equal to an integral number of deBroglie wavelength so that constructive interference may take place i.e. 2πr = nλ

But λ = h/p

∴ L = r p = nh/2π (Bohr’* quantization condition) (1)