At t=O, light of intensity `10^(12)` photons/` s-m^(2)` of energy 6eV per photon starts falling on a plate with work founction `2.5 eV` If area of the plate is `2xx10^(-4) m^(2)` and for every `10^(5)` photons one photoelectron is emitted, charge on the plate at t=25 s is

Options

A. `8xx10^(-15) C`
B. `4xx10^(-14) C`
C. `12xx10^(-10) C`
D. `16xx10^(-12) C`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the number of photons incident on the plate in 25 seconds.

Given:
- Intensity of light = \(10^{12}\) photons/s-m²
- Area of the plate = \(2 \times 10^{-4}\) m²
- Time = 25 s

The number of photons incident on the plate can be calculated using the formula:

\[ \text{Number of photons} = \text{Intensity} \times \text{Area} \times \text{Time} \]

Substituting the values:

\[ \text{Number of photons} = 10^{12} \, \text{photons/s-m}^2 \times 2 \times 10^{-4} \, \text{m}^2 \times 25 \, \text{s} \]

Calculating this:

\[ \text{Number of photons} = 10^{12} \times 2 \times 10^{-4} \times 25 = 50 \times 10^{8} = 5 \times 10^{9} \, \text{photons} \]

### Step 2: Calculate the number of photoelectrons emitted.

According to the problem, for every \(10^{5}\) photons, one photoelectron is emitted. Therefore, the number of photoelectrons emitted can be calculated as:

\[ \text{Number of photoelectrons} = \frac{\text{Number of photons}}{10^{5}} \]

Substituting the number of photons calculated in Step 1:

\[ \text{Number of photoelectrons} = \frac{5 \times 10^{9}}{10^{5}} = 5 \times 10^{4} \]

### Step 3: Calculate the total charge on the plate.

The charge of one electron is approximately \(1.6 \times 10^{-19}\) coulombs. Therefore, the total charge \(Q\) on the plate can be calculated using:

\[ Q = \text{Number of photoelectrons} \times \text{Charge of one electron} \]

Substituting the values:

\[ Q = 5 \times 10^{4} \times 1.6 \times 10^{-19} \]

Calculating this:

\[ Q = 8 \times 10^{-15} \, \text{coulombs} \]

### Final Answer:

The charge on the plate at \(t = 25\) seconds is \(8 \times 10^{-15}\) coulombs.

---