If one were to apply Bohr model to a particle 'm' and charge 'q' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the nth level will be?

2πrn = nλ = nh/p.. (1)
qvB = mv²/r (2)
From (2) v = qBr/m
Substituting in (1), we get
2πr = nh/mv = nhm/qBr
r = nhm/2πqB
Energy E = 1/2mv² = 1/2m(qBr/m)² = q²B²r²/2m
Substituting r, we get
E = q²B²/2m (nhm/2πqB)² = n²(h²q²/4π²m)(1/2m) = n²(h²q²/8π²m²)
E = n²(hqB/4πm)²
E = n²(h²q²B²/16π²m²)
E = n²(hqB/4πm)