Find relation for Bohr magneton. - Vidyadip

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Find relation for Bohr magneton.

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Answer

Relation for Bohr magneton:
a. According to Bohr's theory, an electron in an atom can revolve only in certain stationary orbits in which angular momentum $( L )$ of the electron is an integral multiple (n) of $\frac{h}{2 \pi}$, where $h$ is Planck's constant.
$
\therefore L = m _{ e } vr =\frac{ nh }{2 \pi}
$
b. The orbital magnetic momentum of an electron is given as, $m _{\text {orb }}=\frac{ eL }{2 m _{ e }}$
c. Substituting equation (1) and (2), we have,
$
m _{ orb }= n \left(\frac{ eh }{4 \pi m _{ e }}\right)
$
d. For the $1^{\text {st }}$ orbit, $n =1$,
$
\therefore m _{ orb }=\frac{ eh }{4 \pi m _{ e }}
$
e. The quantity $\frac{\text { eh }}{4 \pi m _{ e }}$ is called Bohr Magneton and its value is $9.274 \times 10^{-24} Am ^2$.
$f$. The magnetic moment of an atom is stated in terms of Bohr magnetons (B.M.).

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