Light of wavelength 3000 `Å` falls on a sensitive surface. If the surface has received `10^-7` J of energy, then the number of photons falling on the surface area is

Options

A. `5 xx 10^(11)`
B. `2.5 xx 10^(11)`
C. `3 xx 10^(11)`
D. None of these

Answer

To find the number of photons falling on the surface when light of wavelength 3000 Å (angstroms) falls on it and the surface receives \(10^{-7}\) J of energy, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Wavelength (\(\lambda\)) = 3000 Å = \(3000 \times 10^{-10}\) m = \(3 \times 10^{-7}\) m
- Total energy received (\(E_T\)) = \(10^{-7}\) J

2. **Calculate the energy of one photon:**
The energy of one photon (\(E\)) can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(h\) (Planck's constant) = \(6.63 \times 10^{-34}\) J·s
- \(c\) (speed of light) = \(3 \times 10^{8}\) m/s

3. **Substituting the values into the formula:**
\[ E = \frac{(6.63 \times 10^{-34} \text{ J·s}) \times (3 \times 10^{8} \text{ m/s})}{3 \times 10^{-7} \text{ m}} \]

4. **Calculating the energy of one photon:**
\[ E = \frac{(6.63 \times 3) \times 10^{-34 + 8 + 7}}{3} \]
\[ E = \frac{19.89 \times 10^{-19}}{3} = 6.63 \times 10^{-19} \text{ J} \]

5. **Calculate the number of photons (\(N\)):**
The number of photons can be found using the formula:
\[ N = \frac{E_T}{E} \]
Substituting the values:
\[ N = \frac{10^{-7} \text{ J}}{6.63 \times 10^{-19} \text{ J}} \]

6. **Perform the calculation:**
\[ N = \frac{10^{-7}}{6.63 \times 10^{-19}} \approx 1.51 \times 10^{11} \]

### Final Answer:
The number of photons falling on the surface is approximately \(1.51 \times 10^{11}\).

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