Question

How is the angular momentum value (mvr=h/2 pi) in Bohrs atomic theory (postulates) calculated? Please explain it in an easy way.

Answer 1

Actually, angular momentum value (mvr=nh/2 pi) not h/2pi.Coming to the point, Firstly, this formula was not derived by anyone. It was observed by BOHR from an experiment. Later it was proved by Albert Einstein with the help of De Broglie Equation. According to de Broglie,

Wavelength(w) = h/mv       ---(I)

and from equation derived after de Broglie eqn:-

nw = 2 pi r       ---------------(II)

where n is number of wave, w is de Broglie wavelength, r is radius of shell.From equation I and II,

n(h/mv) = 2 pi r         (putting the value of w from eqn I to II)

After simplifying we get,

Angular Momentum = mvr = nh/2 pi

PROVED