If the potential differenceappliedtoan X-raytubeis `5 kV` and the current through it is `6.4mA`, then number of electrons striking the target per second is `y times 10^(16)`. Find `y`.

Answer

To find the number of electrons striking the target per second in an X-ray tube given the potential difference and current, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Potential difference (V) = 5 kV = \(5 \times 10^3\) V
- Current (I) = 6.4 mA = \(6.4 \times 10^{-3}\) A

2. **Use the Formula for Current:**
The current (I) is defined as the charge (Q) flowing per unit time (T):
\[ I = \frac{Q}{T} \]
Here, \(Q\) is the total charge of electrons striking the target in time \(T\).

3. **Relate Charge to Number of Electrons:**
The charge \(Q\) can also be expressed in terms of the number of electrons (n) and the charge of a single electron (e):
\[ Q = n \cdot e \]
where \(e\) (the charge of an electron) = \(1.6 \times 10^{-19}\) C.

4. **Combine the Equations:**
Substituting \(Q\) in the current equation gives:
\[ I = \frac{n \cdot e}{T} \]
Since we are interested in the number of electrons per second, we set \(T = 1\) second:
\[ I = n \cdot e \]

5. **Solve for n:**
Rearranging the equation for \(n\):
\[ n = \frac{I}{e} \]

6. **Substitute the Values:**
Now, substituting the values of \(I\) and \(e\):
\[ n = \frac{6.4 \times 10^{-3}}{1.6 \times 10^{-19}} \]

7. **Calculate n:**
Performing the calculation:
\[ n = \frac{6.4 \times 10^{-3}}{1.6 \times 10^{-19}} = 4 \times 10^{16} \]

8. **Identify y:**
The question states that the number of electrons striking the target per second is \(y \times 10^{16}\). From our calculation, we see:
\[ n = 4 \times 10^{16} \implies y = 4 \]

### Final Answer:
Thus, the value of \(y\) is \(4\).

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