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Question
Derive the quantity for Bohr magneton and also state its value.
Solution
- 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 `h/(2pi)`, where h is Planck’s constant.
∴ L = mevr = `"nh"/(2pi)` ….(1) - The orbital magnetic momentum of an electron is given as, morb = `("eL")/(2"m"_"e")` .....….(2)
- Substituting equation (1) and (2), we have,
morb = `"n"("eh"/(4pi"m"_"e"))` - For the 1st orbit, n = 1,
∴ morb = `"eh"/(4pi"m"_"e")` - The quantity `"eh"/(4pi"m"_"e")` is called Bohr Magneton and its value is 9.274 × 10-24 Am2.
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