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What does this means... Angular momentum is quantised i.e it us an integral multiple of h/2π
Asked by ghanghoriashreyastha | 02 Jan, 2019, 08:06: PM
answered-by-expert Expert Answer
when an electron of mass m is orbiting in a circular orbit of radius r with speed v, its angular momentum is given by
 
L = m×v×r   .........................(1)
 
according to de-broglie, electrons have dual nature of behaviour and behaves like particle and wave.
If electron has momentum mv, then its wavelength λ is given by
 
λ = h/(mv)   ..................................(2)
 
where h is plancks constant.
 
When Bohr developed his theory of hydrogen atom, it was stated that electrons revolving in stationary orbit
will never loose energy and this stationary orbit satisfies the condition that the circumference of orbit is
integral multiples of wavelength.
 
Hence 2πr = nλ .....................(3)
 
if we combine all equations (1), (2) and (3),  angular momentum L = (h/λ)×(nλ)/2π = n ×(h/2π)
 
where n is called orbital quantum number. For ground state n = 1, first excited state n = 2 and so on
 
Hence quantisation of angular momentum is integral multple of h/2π .
The quantity h/2π is multipled by integers and no fraction is involved.

Orbital quantum number n  depends upon whether the electron is in ground state or excited state.
Answered by Thiyagarajan K | 03 Jan, 2019, 10:18: AM

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