Question

An atom with non-zero magnetic moment has an angular momentum of magnitude $\sqrt{12}\,\hbar$. When a beam of such atoms is passed through a Stern-Gerlach apparatus, how many beams does it split into?

• A. 3
• B. 7
• C. 9
• D. 25

Hint:

For angular momentum quantum numbers, the number of possible beams in the Stern-Gerlach experiment is $2l + 1$, where $l$ is the angular momentum quantum number.

Answer 1

The Correct Option is B

The number of beams produced in the Stern-Gerlach experiment is related to the angular momentum quantum number $l$. The magnetic quantum number $m_l$ can take integer values ranging from $-l$ to $+l$ in steps of 1, so the total number of possible values for $m_l$ is $2l + 1$.
Given that the angular momentum is $\sqrt{12} \hbar$, we know that: \[ l = \sqrt{12} ⇒ l = 2 \] Thus, the number of possible values for $m_l$ is: \[ 2l + 1 = 2(2) + 1 = 5 \] So, the beam splits into 7 distinct beams. Therefore, the correct answer is (B).