Question

The gyromagnetic ratio of electron is ______.

Options

• `(2m_e)/e`

• `(2m_e)/(e^2)`

• `e/(2m_e)`

• `(e^2)/(2m_e)`

Answer 1

The gyromagnetic ratio of electron is `bbunderline(e/(2m_e))`.

Explanation:

The gyromagnetic ratio (γ) is defined as the ratio of an object’s magnetic dipole moment (μ) to its angular momentum (L).

For an electron moving in a circle,

μ = I . A

= `(ev)/(2pir)*(pir^2)`

= `(evr)/2`

For the same electron, L = m_evr

When you divide the magnetic moment by the angular momentum:

`γ = μ/L`

= `((evr)/2)/(m_evr)`

= `(evr)/2 xx 1/(m_evr)`

= `e/(2m_e)`