Question

An electron is revolving in a circular orbit of radius 'r' in hydrogen atom. Using Bohr's theory, the angular momentum of the electron is
(M = magnetic dipole moment, m = mass of electron)

• A. \(\frac{mM}{e}\)
• B. \(\frac{e}{mM}\)
• C. \(\frac{2mM}{e}\)
• D. \(\frac{e}{2mM}\)

Hint:

Express the magnetic moment through the orbital current, then relate it to angular momentum m v r.

Answer 1

The Correct Option is C

Step 1: Use the gyromagnetic ratio.
For an orbiting charge, $\dfrac{M}{L} = \dfrac{e}{2m}$.

Step 2: Rearrange.
$L = \dfrac{2m}{e}M$.

Step 3: Verify.
Using $M = \dfrac{evr}{2}$ and $L = mvr$ gives $\dfrac{M}{L} = \dfrac{e}{2m}$, the same result.

Final Answer:
Option (C). \[ \boxed{\frac{2mM}{e}} \]