The photosensitive surface is receiving the light of wavelength `5000Å` at the rate of `10^(-8)"J s"^(-1)`. The number of photons received per second is `(h=6.62xx10^(-34)Js, c=3xx10^(8)ms^(-1))`

Options

A. `2.5xx10^(5)`
B. `2.5xx10^(11)`
C. `2.5xx10^(12)`
D. `2.5xx10^(9)`

Answer

To solve the problem, we need to determine the number of photons received per second by a photosensitive surface when exposed to light of a specific wavelength and power.

### Step-by-Step Solution:

1. **Identify Given Values**:
- Wavelength (λ) = 5000 Å = 5000 × 10^(-10) m (since 1 Å = 10^(-10) m)
- Power (P) = 10^(-8) J/s
- Planck's constant (h) = 6.62 × 10^(-34) J·s
- Speed of light (c) = 3 × 10^(8) m/s

2. **Use the Energy of a Photon Formula**:
The energy (E) of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]

3. **Calculate Energy of a Single Photon**:
Substitute the values of h, c, and λ into the formula:
\[ E = \frac{(6.62 \times 10^{-34} \text{ J·s})(3 \times 10^{8} \text{ m/s})}{5000 \times 10^{-10} \text{ m}} \]

Simplifying this:
\[ E = \frac{(6.62 \times 3) \times 10^{-34 + 8}}{5000 \times 10^{-10}} \]
\[ E = \frac{19.86 \times 10^{-26}}{5000 \times 10^{-10}} = \frac{19.86 \times 10^{-26}}{5 \times 10^{-7}} = \frac{19.86}{5} \times 10^{-19} = 3.972 \times 10^{-19} \text{ J} \]

4. **Calculate the Number of Photons per Second**:
The number of photons (n) received per second can be calculated using the formula:
\[ n = \frac{P}{E} \]
Substitute the values of P and E:
\[ n = \frac{10^{-8} \text{ J/s}}{3.972 \times 10^{-19} \text{ J}} \]

Performing the calculation:
\[ n \approx \frac{10^{-8}}{3.972 \times 10^{-19}} \approx 2.51 \times 10^{10} \text{ photons/s} \]

5. **Final Result**:
The number of photons received per second is approximately \(2.51 \times 10^{10}\).