A uniform magnetic field B is present in a region. An electron is...

When an electron moves in a circular path perpendicular to a uniform magnetic field, the magnetic force provides the necessary centripetal force:

$\dfrac{mv^2}{r} = evB$

$mv = eBr$

According to Bohr's quantization rule for angular momentum:

$mvr = \dfrac{nh}{2\pi}$

Substituting $mv = eBr$ into the quantization condition:

$(eBr)r = \dfrac{nh}{2\pi}$

$eBr^2 = \dfrac{nh}{2\pi}$

$r = \sqrt{\dfrac{nh}{2\pi eB}}$

For the smallest possible radius, the principal quantum number $n$ must be minimum, which is $n = 1$. Substituting $n = 1$:

$r = \sqrt{\dfrac{h}{2\pi eB}}$