The electron with change `(q=1.6xx10^(-19)C)` moves in an orbit of radius `5xx10^(-11)`m with a speed of `2.2xx10^(6)ms^(-1)`, around an atom. The equivalent current is

Options

A. `1.12xx10^(-6)A`
B. `1.12xx10^(-3)A`
C. `1.12xx10^(-9)A`
D. `1.12A`

Answer

To find the equivalent current produced by an electron moving in an orbit, we can follow these steps:

### Step 1: Identify the given values
- Charge of the electron, \( q = 1.6 \times 10^{-19} \, \text{C} \)
- Radius of the orbit, \( r = 5 \times 10^{-11} \, \text{m} \)
- Speed of the electron, \( v = 2.2 \times 10^{6} \, \text{m/s} \)

### Step 2: Calculate the time period \( T \) for one complete revolution
The time period \( T \) can be calculated using the formula:
\[ T = \frac{2 \pi r}{v} \]

Substituting the values:
\[ T = \frac{2 \times 3.14 \times (5 \times 10^{-11})}{2.2 \times 10^{6}} \]
Calculating the numerator:
\[ 2 \times 3.14 \times 5 \times 10^{-11} = 31.4 \times 10^{-11} = 3.14 \times 10^{-10} \, \text{m} \]
Now substituting into the equation for \( T \):
\[ T = \frac{3.14 \times 10^{-10}}{2.2 \times 10^{6}} \approx 1.427 \times 10^{-16} \, \text{s} \]

### Step 3: Calculate the equivalent current \( I \)
The equivalent current \( I \) can be calculated using the formula:
\[ I = \frac{q}{T} \]

Substituting the values:
\[ I = \frac{1.6 \times 10^{-19}}{1.427 \times 10^{-16}} \]
Calculating the current:
\[ I \approx 1.12 \times 10^{-3} \, \text{A} \]

### Conclusion
The equivalent current produced by the electron moving in its orbit is approximately:
\[ I \approx 1.12 \times 10^{-3} \, \text{A} \]