Question

Derive the quantity for Bohr magneton and also state its value.

Answer 1

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_evr = `"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.