Question

An electron of mass '\(m_{e}\)' and charge '\(e\)' revolving around the nucleus in \(n^{th}\) orbit has orbital magnetic moment \(\frac{enh}{4\pi m_{e}}\) which is equal to Bohr Magneton, the orbit number in which electron should revolve is (\(h\) = Planck's constant)

• A. four
• B. three
• C. two
• D. one

Hint:

Compare the given magnetic moment expression with the Bohr magneton, which is its value for n = 1.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The orbital magnetic moment of an electron in the n-th Bohr orbit is \(\mu = \dfrac{neh}{4\pi m_{e}}\).

Step 2: Bohr magneton
The Bohr magneton is the value for the first orbit: \(\mu_{B} = \dfrac{eh}{4\pi m_{e}}\).

Step 3: Calculation
Set \(\dfrac{neh}{4\pi m_{e}} = \dfrac{eh}{4\pi m_{e}}\). This gives \(n=1\).

Final Answer:
The electron must be in the first orbit. \[ \boxed{\text{(D) }\text{one}} \]