Question 412: Atoms & Nuclei

Question

The magnetic moment of electron due to orbital motion is proportional to ( $\mathrm{n}=$ principal quantum number)

Accepted Answer

Step 1. Recall expression for orbital magnetic moment
An electron in the $n$th Bohr orbit has current loop behavior. The orbital magnetic moment is
$ \mu = \frac{e}{2m} L, $
where $L$ is the orbital angular momentum.
Step 2. Angular momentum in Bohr model
From BohrÃ¢ÂÂs quantization condition:
$ L_n = n \hbar. $
So,
$ \mu_n = \frac{e}{2m} (n\hbar). $
Step 3. Relation to Bohr magneton
$ \mu_B = \frac{e \hbar}{2m}. $
So,
$ \mu_n = n \mu_B. $
Answer:
The orbital magnetic moment is
proportional to $n$
.
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Correct option: A. $n$

Answer

n

Answer

$n^2$

Answer

$\frac{1}{n}$

Answer

$\frac{1}{\mathrm{n}^2}$

Atoms & Nuclei

The magnetic moment of electron due to orbital motion is proportional to ( \mathrm{n}= principal quantum number)

Choose the correct answer: