Question

Bohr model is applied to a particle of mass 'm' and charge 'q' is moving in a plane under the influence of a transverse magnetic field 'B. The energy of the charged particle in the nth level will be (h = Planck's constant).

Options

• 2nhq B/π m

• nhq B/2π m

• nhq B/4π m

• nhq B/π m

Answer 1

nhq B/4π m

Explanation:

For a particle moving in a magnetic field, then applied two forces are equal.

centripetal force (F_c) = magnetic force (F_m)

`=> "mv"^2/"r" = "qvB"`

`=> "mv"^2 = "qB"("vr")`     ....(i)

Also, from Bohr's model,

mvr = `"nh"/(2pi)`

`therefore "vr" = "nh"/(2pi"m")`    ...(ii)

From Eq. (i) and (ii), we get

`"mv"^2 = "nh"/(2pi"m") * "qB"`   ....(iii)

Energy of the electron moving in nth orbit,

E = `1/2 * "mv"^2 = 1/2 * ("nhqB"/(2pi"m"))`   ....(Using Eq. (iii))

`=> "E" = "nhqB"/(4pi"m")`

Hence, the energy of the charged particle in the nth level will be `"nhqB"/(4pi"m")`.