Question

A model for quantised motion of an electron in a uniform magnetic field B states that the flux passing through the orbit of the electron is n(h/e) where n is an integer, h is Planck’s constant and e is the magnitude of electron’s charge. According to the model, the magnetic moment of an electron in its lowest energy state will be (m is the mass of the electron):

Options

• `(he)/(pim)`

• `(he)/(2pim)`

• `(heB)/(pim)`

• `(heB)/(2pim)`

Answer 1

`(he)/(2pim)`

Explanation:

Magnetic flux ΦB = B(πr²) 

= `(nh)/e`   ...(i)

Magnetic moment `|barM| = i(pir^2)`

= `e/T(pir^2)`

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

= `(ev(pir^2))/(2pi((mv)/(eB)))`

= `(e^2B(pir^2))/(2pim)`

= `e^2/(2pi) xx (mv)/(eB)`

From (i) putting

n = 1

`|barM| = (eh)/(2pim)`