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Question
Find relation for Bohr magneton.
Solution
Relation for Bohr magneton:
- 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 = `"m"_"e""vr" = "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.
- The magnetic moment of an atom is stated in terms of Bohr magnetons (B.M.).
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