Question

In hydrogen atom, an electron of charge 'e' revolves in an orbit of radius 'r' with speed 'v'. The magnetic moment associated with electron is

• A. \( \frac{evr}{3} \)
• B. \( \frac{evr}{2} \)
• C. evr
• D. \( \sqrt{2}evr \)

Hint:

The ratio of magnetic moment to angular momentum ($L = mvr$) is constant: $\frac{M}{L} = \frac{e}{2m}$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
A moving charge constitutes a current. A current loop has a magnetic dipole moment.
Step 2: Key Formula or Approach:
Magnetic Moment \( M = I \times A \).
Current \( I = \frac{e}{T} \), where \( T \) is the time period.
Step 3: Detailed Explanation:
Time period \( T = \frac{2\pi r}{v} \).
Current \( I = \frac{e}{2\pi r / v} = \frac{ev}{2\pi r} \).
Area of the loop \( A = \pi r^2 \).
Magnetic Moment \( M = \left( \frac{ev}{2\pi r} \right) \times \pi r^2 = \frac{evr}{2} \).
Step 4: Final Answer:
The magnetic moment is \( \frac{evr}{2} \).