If an electron revolves in the circular path of radius `0.5A^(@)` at a frequency of `5xx10^(15)` cycles/sec. The equivalent electric current is (charge of an electron=1.6x10^-19)

Explanation

To solve the problem, we need to find the equivalent electric current produced by an electron revolving in a circular path. We can use the formula for electric current, which is defined as the rate of flow of charge.

### Step-by-Step Solution:

1. **Identify the given values**:
- Radius of the circular path, \( r = 0.5 \) Å (angstrom) = \( 0.5 \times 10^{-10} \) m (since \( 1 \) Å = \( 10^{-10} \) m)
- Frequency of revolution, \( f = 5 \times 10^{15} \) cycles/sec
- Charge of an electron, \( Q = 1.6 \times 10^{-19} \) C (coulombs)

2. **Recall the formula for electric current**:
The electric current \( I \) can be expressed as:
\[ I = \frac{Q}{T} \]
where \( T \) is the time period of one complete cycle. However, we can also express current in terms of frequency:
\[ I = Q \cdot f \]
because frequency \( f \) is the reciprocal of the time period \( T \) (i.e., \( f = \frac{1}{T} \)).

3. **Substitute the values into the formula**:
Now, we can substitute the values of \( Q \) and \( f \) into the equation:
\[ I = (1.6 \times 10^{-19} \, \text{C}) \cdot (5 \times 10^{15} \, \text{cycles/sec}) \]

4. **Calculate the current**:
\[ I = 1.6 \times 5 \times 10^{-19} \times 10^{15} \]
\[ I = 8 \times 10^{-4} \, \text{A} \]

5. **Convert the current to milliampere**:
Since \( 1 \, \text{mA} = 10^{-3} \, \text{A} \):
\[ I = 8 \times 10^{-4} \, \text{A} = 0.8 \, \text{mA} \]

### Final Answer:
The equivalent electric current is \( 0.8 \, \text{mA} \).