Question

The magnetic moment of the ground state of an atom whose open sub-shell is half-filled with five electrons is

• A. \( \sqrt{35} \, \mu_B \)
• B. \( 35 \, \mu_B \)
• C. \( 35 \, \mu_B \)
• D. \( \mu_B \sqrt{35} \)

Hint:

For magnetic moment in atomic physics, use \( \mu = \sqrt{n(n+2)} \mu_B \) for unpaired electrons.

Answer 1

The Correct Option is D

Step 1: Identify the ground state of the atom.
The magnetic moment of an atom in a ground state is given by \( \mu = \sqrt{n(n+2)} \mu_B \) where \( n \) is the number of electrons in the unpaired orbital. In this case, the number of unpaired electrons is 5. Thus, we apply the formula: \[ \mu = \sqrt{5(5+2)} \mu_B = \mu_B \sqrt{35} \]
Step 2: Conclusion.
Hence, the correct answer is option (D).

Final Answer: \[ \boxed{\mu_B \sqrt{35}} \]