Question

Using de Broglie’s hypothesis, obtain the mathematical form of Bohr’s second postulate.

Answer 1

1. De Broglie suggested that instead of considering the orbiting electrons inside atoms as particles, they should be viewed as standing waves. Also, the length of the orbit of an electron should be an integral multiple of its wavelength.
2. Now, the distance travelled by an electron in one complete revolution in n^th orbit of radius r_n is 2πr_n and it should be an integral multiple of the wavelength.  
   ∴ 2πr_n = nλ   ....(1)
   where, n = 1, 2, 3, 4….
3. By de Broglie hypothesis,
   `lambda = "h"/"p"_"n" = "h"/("m"_"e""v"_"n")`
4. Substituting this value of ‘λ’ in equation (1),
   momentum of electron, p_n = `"nh"/(2pi"r"_"n")`
   ∴ Angular momentum of electron L_n = p_nr_n = `"nh"/(2pi)`
   Thus, the mathematical form of Bohr's second postulate is obtained.