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 find the number of photons received per second by the photosensitive surface, we can follow these steps:

### Step 1: Understand the relationship between power, energy, and photons
The power \( P \) received by the surface is given as \( 10^{-8} \, \text{J/s} \). Power is defined as the energy received per unit time.

### Step 2: Write the formula for energy of photons
The energy \( E \) of a single photon can be expressed using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) is Planck's constant (\( 6.62 \times 10^{-34} \, \text{Js} \)),
- \( c \) is the speed of light (\( 3 \times 10^{8} \, \text{m/s} \)),
- \( \lambda \) is the wavelength of light (in meters).

### Step 3: Convert the wavelength from angstroms to meters
Given the wavelength \( \lambda = 5000 \, \text{Å} \):
\[ \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \]

### Step 4: Calculate the energy of a single photon
Substituting the values into the energy formula:
\[ E = \frac{(6.62 \times 10^{-34} \, \text{Js}) \times (3 \times 10^{8} \, \text{m/s})}{5 \times 10^{-7} \, \text{m}} \]
Calculating this gives:
\[ E = \frac{1.986 \times 10^{-25} \, \text{J}}{5 \times 10^{-7}} = 3.972 \times 10^{-19} \, \text{J} \]

### Step 5: Calculate the number of photons per second
Using the power and the energy of a single photon, we can find the number of photons \( n \) received per second:
\[ n = \frac{P}{E} \]
Substituting the values:
\[ n = \frac{10^{-8} \, \text{J/s}}{3.972 \times 10^{-19} \, \text{J}} \approx 2.52 \times 10^{10} \, \text{photons/s} \]

### Final Answer
The number of photons received per second is approximately \( 2.52 \times 10^{10} \, \text{photons/s} \).

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