The current due to orbital motion of `e^(-)` which is moving around hydrogen atom of radius `0.51xx10^(-10)m` with velocity `2xx10^5m//s`, is:

Options

A. `10^(-1)A`
B. `10^(-2)A`
C. `10^(-3)A`
D. `10^(-4)A`

Explanation

To find the current due to the orbital motion of an electron around a hydrogen atom, we can use the formula for current (I) in terms of charge (q), velocity (v), and the radius (r) of the orbit:

\[ I = \frac{q \cdot v}{2 \pi r} \]

### Step-by-Step Solution:

1. **Identify the given values**:
- Charge of the electron, \( q = 1.6 \times 10^{-19} \) coulombs
- Velocity of the electron, \( v = 2 \times 10^5 \) m/s
- Radius of the hydrogen atom, \( r = 0.51 \times 10^{-10} \) m

2. **Substitute the values into the formula**:
\[ I = \frac{(1.6 \times 10^{-19}) \cdot (2 \times 10^5)}{2 \pi (0.51 \times 10^{-10})} \]

3. **Calculate the denominator**:
- First, calculate \( 2 \pi r \):
\[ 2 \pi (0.51 \times 10^{-10}) \approx 2 \times 3.14 \times 0.51 \times 10^{-10} \approx 3.24 \times 10^{-10} \text{ m} \]

4. **Calculate the numerator**:
\[ (1.6 \times 10^{-19}) \cdot (2 \times 10^5) = 3.2 \times 10^{-14} \text{ C m/s} \]

5. **Now substitute back into the current formula**:
\[ I = \frac{3.2 \times 10^{-14}}{3.24 \times 10^{-10}} \]

6. **Perform the division**:
\[ I \approx 0.09877 \text{ A} \approx 10^{-2} \text{ A} \]

7. **Final Result**:
The current due to the orbital motion of the electron is approximately \( 10^{-2} \) A, which corresponds to option 2.