An electron of mass ' m_e ' and charge ' e ' revolving around the...

The orbital magnetic moment of an electron revolving in the $n^{th}$ orbit is given by $M = \dfrac{n e h}{4 \pi m_e}$.

The Bohr Magneton is defined as the orbital magnetic moment of an electron in the first orbit ($n=1$), which is $\mu_B = \dfrac{e h}{4 \pi m_e}$.

Given that the orbital magnetic moment is equal to the Bohr Magneton:

$\dfrac{n e h}{4 \pi m_e} = \dfrac{e h}{4 \pi m_e}$

$\Rightarrow n = 1$

Thus, the electron should revolve in the first orbit.

Answer: one