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Question
State Bohr's postulate to define stable orbits in the hydrogen atom. How does de Broglie's hypothesis explain the stability of these orbits?
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Solution
According to Bohr, electrons revolve around the nucleus only in those discrete orbits which are non-radiating and for which the angular momentum of the revolving electron is an integral multiple of `h/(2pi)`. These discrete orbits are known as stationary or stable orbits
According to de Broglie, a stationary orbit is that which contains an integral number of de Broglie waves associated with the revolving electron.
For an electron revolving in nth circular orbit of radius rn,
Total distance covered = circumference of the orbit = `2pir_n`
Therefore, for the permissible orbit, `2pir_n= nlambda`
According to de Broglie, `lambda = h/(mv_n)`
where vn is the speed of electron revolving in nth orbit.
Therefore
`2pir_n = (nh)/(mv_n)`
or
`mv_nr_n = (nh)/(2pi) = n(h/(2pi))`
Thus, angular momentum of electron revolving in nth orbit must be an integral multiple of `h/(2pi)` which is same as proposed by bohr's second postulate defining stable orbits.
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