X - rays can generated by accelerating electrons in a vacuum and letting them impact on atoms in a metal surface. If the 1000 eV kinetic energy of the electrons is completely converted to photon energy. If the electron current is `1.5xx10^(-5)A`, how many photons are produced in `10^(-10)` second?

Options

A. 9375 photons
B. 1000 photons
C. 8687 photons
D. 1610 photons

Answer

To solve the problem, we need to determine how many photons are produced when electrons with a certain current and kinetic energy impact a metal surface. Here’s the step-by-step solution:

### Step 1: Calculate the total charge (Q) produced in the given time (t).
The formula for charge is given by:
\[ Q = I \times t \]
Where:
- \( I \) is the current (in Amperes)
- \( t \) is the time (in seconds)

Given:
- \( I = 1.5 \times 10^{-5} \, \text{A} \)
- \( t = 10^{-10} \, \text{s} \)

Substituting the values:
\[ Q = (1.5 \times 10^{-5} \, \text{A}) \times (10^{-10} \, \text{s}) \]
\[ Q = 1.5 \times 10^{-15} \, \text{C} \]

### Step 2: Calculate the number of electrons (n) corresponding to the total charge (Q).
The charge of one electron (e) is:
\[ e = 1.6 \times 10^{-19} \, \text{C} \]

The number of electrons can be calculated using the formula:
\[ n = \frac{Q}{e} \]

Substituting the values:
\[ n = \frac{1.5 \times 10^{-15} \, \text{C}}{1.6 \times 10^{-19} \, \text{C}} \]
\[ n = 9.375 \times 10^{3} \]

### Step 3: Determine the number of photons produced.
According to the problem, all the kinetic energy of the electrons is converted into photon energy. Therefore, the number of photons produced is equal to the number of electrons.

Thus, the number of photons produced is:
\[ \text{Number of photons} = n = 9.375 \times 10^{3} \]

### Final Answer:
The total number of photons produced in \( 10^{-10} \) seconds is approximately:
\[ 9375 \, \text{photons} \]

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