Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsQuestion Bank [ 2022 ]3 Marks
Question
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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