A uniform magnetic field B is present in a region. An electron is projected perpendicular to the field and moves in a circle. Assuming Bohr's quantization rule for angular momentum, determine the smallest possible radius of the electron.

Step-by-step solution

When an electron moves in a circular path perpendicular to a uniform magnetic field, the magnetic force provides the necessary centripetal force: mv^2 r = evB mv = eBr According to Bohr's quantization rule for angular momentum: mvr = nh 2 Substituting mv = eBr into the quantization condition: (eBr)r = nh 2 eBr^2 = nh 2 r = nh 2 eB For the smallest possible radius, the principal quantum number n must be minimum, which is n = 1 . Substituting n = 1 : r = h 2 eB