In hydrogen atom, the electron is making `6.6xx10^(15) rev//sec` around the nucleus in an orbit of radius `0.528 A`. The magnetic moment `(A-m^(2)) will be

Options

A. `1xx10^(-15)`
B. `1xx10^(-10)`
C. `1xx10^(-23)`
D. `1xx10^(-27)`

Explanation

To find the magnetic moment of an electron in a hydrogen atom, we can follow these steps:

### Step 1: Calculate the Current (I)
The current produced by the revolving electron can be calculated using the formula:
\[ I = n \cdot e \]
where:
- \( n \) is the number of revolutions per second (given as \( 6.6 \times 10^{15} \) rev/sec),
- \( e \) is the charge of the electron (\( 1.6 \times 10^{-19} \) C).

Calculating the current:
\[ I = 6.6 \times 10^{15} \, \text{rev/sec} \times 1.6 \times 10^{-19} \, \text{C} = 1.056 \times 10^{-3} \, \text{A} \]

### Step 2: Calculate the Area (A)
The area of the circular orbit can be calculated using the formula:
\[ A = \pi r^2 \]
where:
- \( r \) is the radius of the orbit (given as \( 0.528 \, \text{Å} = 0.528 \times 10^{-10} \, \text{m} \)).

Calculating the area:
\[ A = \pi \times (0.528 \times 10^{-10})^2 \approx 3.14 \times (0.528^2 \times 10^{-20}) \approx 3.14 \times 0.278784 \times 10^{-20} \approx 0.875 \times 10^{-20} \, \text{m}^2 \]

### Step 3: Calculate the Magnetic Moment (μ)
The magnetic moment can be calculated using the formula:
\[ \mu = I \cdot A \]

Substituting the values we calculated:
\[ \mu = 1.056 \times 10^{-3} \, \text{A} \times 0.875 \times 10^{-20} \, \text{m}^2 \approx 9.24 \times 10^{-24} \, \text{A m}^2 \]

### Final Answer
The magnetic moment of the electron in the hydrogen atom is approximately:
\[ \mu \approx 9.24 \times 10^{-24} \, \text{A m}^2 \]

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