In a certain particle accelerator, electrons emerge in pulses at the rate of 250 pulses pe second. Each pulse is of duration of 200 ns and the electrons in the pulse constitute a current of 250 mA. The number of electrons delivered by the accelerator per pulse is

Options

A. `8.00xx10^(10)`
B. `5.00xx10^(8)`
C. `3.13xx10^(11)`
D. `9.60xx10^(10)`

Explanation

To solve the problem of finding the number of electrons delivered by the accelerator per pulse, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Current (I) = 250 mA = 250 × 10^(-3) A
- Duration of each pulse (t) = 200 ns = 200 × 10^(-9) s

2. **Calculate the charge (dq) delivered in one pulse:**
- The relationship between current, charge, and time is given by the formula:
\[ I = \frac{dq}{dt} \]
- Rearranging this gives:
\[ dq = I \cdot dt \]
- Substituting the values:
\[ dq = (250 \times 10^{-3} \, \text{A}) \cdot (200 \times 10^{-9} \, \text{s}) \]
- Performing the multiplication:
\[ dq = 250 \times 200 \times 10^{-3} \times 10^{-9} = 5 \times 10^{-8} \, \text{C} \]

3. **Calculate the number of electrons (n) delivered per pulse:**
- The charge of a single electron (e) is approximately:
\[ e = 1.6 \times 10^{-19} \, \text{C} \]
- The number of electrons can be calculated using the formula:
\[ n = \frac{dq}{e} \]
- Substituting the values:
\[ n = \frac{5 \times 10^{-8} \, \text{C}}{1.6 \times 10^{-19} \, \text{C/electron}} \]
- Performing the division:
\[ n = \frac{5}{1.6} \times 10^{11} \approx 3.125 \times 10^{11} \]
- Rounding this gives:
\[ n \approx 3.13 \times 10^{11} \]

4. **Conclusion:**
- The number of electrons delivered by the accelerator per pulse is approximately \(3.13 \times 10^{11}\).

### Final Answer:
The number of electrons delivered by the accelerator per pulse is \(3.13 \times 10^{11}\).

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