Question

Find relation for Bohr magneton.

Answer 1

Relation for Bohr magneton:

1. 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)
2. The orbital magnetic momentum of an electron is given as, m_orb = `"eL"/(2"m"_"e")` ….(2)
3. Substituting equation (1) and (2), we have,
   m_orb = n`("eh"/(4pi"m"_"e"))`
4. For the 1^st orbit, n = 1,
   ∴ m_orb = `"eh"/(4pi"m"_"e")`
5. The quantity `"eh"/(4pi"m"_"e")` is called Bohr Magneton and its value is 9.274 × 10^-24 Am². 
6. The magnetic moment of an atom is stated in terms of Bohr magnetons (B.M.).