Define Bohr magneton using Bohr's first hypothesis.

(N/A) Bohr magneton is defined as the magnetic moment associated with an electron due to its orbital motion in the first orbit of a hydrogen atom.
Bohr's first hypothesis states that the angular momentum of an electron in an orbit is quantized and given by:
$L = n \left( \frac{h}{2 \pi} \right)$
where $n = 1, 2, 3, \ldots$ and $h$ is Planck's constant $(h = 6.626 \times 10^{-34} \text{ J s})$.
The magnetic moment $\mu_l$ associated with an orbital electron is given by:
$\mu_l = \frac{e}{2 m_e} L$
Substituting the expression for angular momentum for the first orbit $(n = 1)$:
$\mu_l = \frac{e}{2 m_e} \left( \frac{h}{2 \pi} \right)$
This minimum value of the magnetic moment is called the Bohr magneton $(\mu_B)$:
$\mu_B = \frac{eh}{4 \pi m_e}$
Substituting the values $e = 1.6 \times 10^{-19} \text{ C}$,$h = 6.63 \times 10^{-34} \text{ J s}$,and $m_e = 9.11 \times 10^{-31} \text{ kg}$:
$\mu_B = \frac{(1.6 \times 10^{-19}) \times (6.63 \times 10^{-34})}{4 \times 3.14 \times 9.11 \times 10^{-31}}$
$\mu_B \approx 9.27 \times 10^{-24} \text{ A m}^2$