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

Options

A. `2 xx 10^(16)`
B. `5xx 10^(16)`
C. `1 xx 10^(17)`
D. `4 xx 10^(15)`

Explanation

To find the number of electrons striking the target per second in an X-ray tube, we can use the relationship between current, charge, and the number of electrons. Here's the step-by-step solution:

### Step 1: Understand the relationship between current, charge, and time
The current (I) can be expressed in terms of the number of electrons (n), the charge of an electron (e), and the time interval (t):
\[ I = \frac{n \cdot e}{t} \]
Where:
- \( I \) is the current in amperes (A)
- \( n \) is the number of electrons
- \( e \) is the charge of an electron (approximately \( 1.6 \times 10^{-19} \) coulombs)
- \( t \) is the time in seconds

### Step 2: Rearrange the formula to solve for n
We can rearrange the formula to solve for \( n \):
\[ n = \frac{I \cdot t}{e} \]

### Step 3: Substitute the known values
Given:
- The current \( I = 3.2 \, \text{mA} = 3.2 \times 10^{-3} \, \text{A} \)
- The charge of an electron \( e = 1.6 \times 10^{-19} \, \text{C} \)
- We will consider the time interval \( t = 1 \, \text{s} \)

Substituting these values into the equation:
\[ n = \frac{3.2 \times 10^{-3} \, \text{A} \cdot 1 \, \text{s}}{1.6 \times 10^{-19} \, \text{C}} \]

### Step 4: Calculate n
Now, we perform the calculation:
\[ n = \frac{3.2 \times 10^{-3}}{1.6 \times 10^{-19}} \]

Calculating this gives:
\[ n = 2 \times 10^{16} \]

### Conclusion
The number of electrons striking the target per second is:
\[ n = 2 \times 10^{16} \]

### Final Answer
Thus, the number of electrons striking the target per second is \( 2 \times 10^{16} \).

---