The potential difference applied to an X - ray tube is 5 kV and the current through it is 3.2 . Then the number of electrons striking the target per second is

Options

A. `2xx10^(16)`
B. `5xx10^(16)`
C. `1xx10^(16)`
D. `4xx10^(16)`

Explanation

To solve the problem of finding the number of electrons striking the target per second in an X-ray tube with a potential difference of 5 kV and a current of 3.2 mA, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Current to Amperes**:
The current given is in milliampere (mA). We need to convert it to amperes (A).
\[ I = 3.2 \, \text{mA} = 3.2 \times 10^{-3} \, \text{A} \]

2. **Understand the Relationship Between Current, Charge, and Time**:
The current (I) is defined as the charge (Q) passing through a point per unit time (t):
\[ I = \frac{Q}{t} \]
Here, \(Q\) is the total charge, and \(t\) is the time in seconds.

3. **Calculate Charge per Second**:
If we consider a time interval of 1 second, then the charge passing through is equal to the current:
\[ Q = I \times t = 3.2 \times 10^{-3} \, \text{A} \times 1 \, \text{s} = 3.2 \times 10^{-3} \, \text{C} \]

4. **Determine the Charge of One Electron**:
The charge of one electron (e) is approximately:
\[ e = 1.6 \times 10^{-19} \, \text{C} \]

5. **Calculate the Number of Electrons**:
The number of electrons (n) striking the target per second can be calculated using the total charge divided by the charge of one electron:
\[ n = \frac{Q}{e} = \frac{3.2 \times 10^{-3} \, \text{C}}{1.6 \times 10^{-19} \, \text{C/electron}} \]

6. **Perform the Calculation**:
\[ n = \frac{3.2 \times 10^{-3}}{1.6 \times 10^{-19}} = 2.0 \times 10^{16} \, \text{electrons/second} \]

### Final Answer:
The number of electrons striking the target per second is \(2.0 \times 10^{16}\).

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