An electron in a hydrogen atom makes a transiton from first excited state ot ground state. The magnetic moment due to circulating electron

Options

A. 21
B. 10
C. 15
D. None of these

Explanation

To solve the problem of the magnetic moment due to a circulating electron in a hydrogen atom transitioning from the first excited state to the ground state, we can follow these steps:

### Step 1: Understand the Concept of Magnetic Moment
The magnetic moment (\( \mu \)) of an electron in an atom is related to its angular momentum. For an electron in a circular orbit, the magnetic moment is given by:

\[ \mu \propto L \]

where \( L \) is the angular momentum of the electron.

### Step 2: Angular Momentum in Bohr's Model
According to Bohr's theory, the angular momentum (\( L \)) of an electron in the \( n \)-th orbit is quantized and given by:

\[ L = n \frac{h}{2\pi} \]

where \( n \) is the principal quantum number (the orbit number) and \( h \) is Planck's constant.

### Step 3: Determine the Initial and Final States
In this problem, the electron transitions from the first excited state to the ground state:
- The first excited state corresponds to \( n = 2 \).
- The ground state corresponds to \( n = 1 \).

### Step 4: Calculate the Magnetic Moment for Each State
Using the relationship between angular momentum and magnetic moment, we can express the magnetic moment for both states:
- For the first excited state (\( n = 2 \)):
\[ L_2 = 2 \frac{h}{2\pi} \quad \Rightarrow \quad \mu_2 \propto L_2 \]

- For the ground state (\( n = 1 \)):
\[ L_1 = 1 \frac{h}{2\pi} \quad \Rightarrow \quad \mu_1 \propto L_1 \]

### Step 5: Analyze the Change in Magnetic Moment
Since the angular momentum is directly proportional to the principal quantum number \( n \), we can conclude:
- When the electron transitions from \( n = 2 \) to \( n = 1 \), the magnetic moment decreases because \( n \) is decreasing.

### Conclusion
Thus, the magnetic moment due to the circulating electron decreases when the electron makes a transition from the first excited state to the ground state.

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