To solve the problem of calculating the number of photoelectrons emitted per unit area per second from the surface of a photo metal when light of a specific wavelength and intensity is incident on it, we can follow these steps:
### Step 1: Understand the given data
- Wavelength of light, \( \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \)
- Intensity of light, \( I = 3.96 \times 10^{-3} \, \text{W/cm}^2 = 3.96 \times 10^{-3} \times 10^4 \, \text{W/m}^2 = 3.96 \times 10^{1} \, \text{W/m}^2 \)
- Efficiency of photoelectron emission, \( \text{Efficiency} = 1\% = 0.01 \)
### Step 2: Calculate the energy of one photon
The energy \( E \) of one photon can be calculated using the formula:
\[
E = \frac{hc}{\lambda}
\]
Where:
- \( h = 6.63 \times 10^{-34} \, \text{J s} \) (Planck's constant)
- \( c = 3 \times 10^{8} \, \text{m/s} \) (speed of light)
Substituting the values:
\[
E = \frac{(6.63 \times 10^{-34}) \times (3 \times 10^{8})}{5 \times 10^{-7}}
\]
### Step 3: Calculate the number of photons incident per unit area per second
The number of photons \( N \) incident per unit area per second is given by:
\[
N = \frac{I}{E}
\]
Substituting the values of \( I \) and \( E \) calculated in the previous steps.
### Step 4: Calculate the number of emitted photoelectrons
Since only 1% of the incident photons emit photoelectrons, the number of photoelectrons emitted per unit area per second is:
\[
n = N \times \text{Efficiency}
\]
Substituting the value of \( N \) and the efficiency.
### Step 5: Final Calculation
Now, we can compute the final value of \( n \) to find the number of electrons emitted per unit area per second.
### Detailed Calculation:
1. **Calculate Energy of One Photon**:
\[
E = \frac{(6.63 \times 10^{-34}) \times (3 \times 10^{8})}{5 \times 10^{-7}} = \frac{1.989 \times 10^{-25}}{5 \times 10^{-7}} = 3.978 \times 10^{-19} \, \text{J}
\]
2. **Calculate Number of Photons per Unit Area per Second**:
\[
N = \frac{3.96 \times 10^{1}}{3.978 \times 10^{-19}} \approx 9.95 \times 10^{20} \, \text{photons/m}^2/s
\]
3. **Calculate Number of Electrons Emitted**:
\[
n = N \times 0.01 = 9.95 \times 10^{20} \times 0.01 = 9.95 \times 10^{18} \, \text{electrons/m}^2/s
\]
Thus, the number of electrons emitted per unit area per second from the surface is approximately \( 1 \times 10^{18} \, \text{electrons/m}^2/s \).
### Final Answer:
The number of electrons emitted per unit area per second is \( 1 \times 10^{18} \, \text{electrons/m}^2/s \).
