Find the number of electrons emitted per second by a 24W source of monochromatic light of wavelength ` 6600 Å` , assuming 3 % efficiency for photoelectric effect (take `h= 6.6 xx 10^(-34)Js)`

Options

A. `48xx 10^(19) `
B. ` 48 xx 10^(17)`
C. `8 xx 10^(19)`
D. `24 xx 10^(17)`

Answer

To solve the problem of finding the number of electrons emitted per second by a 24W source of monochromatic light with a wavelength of 6600 Å, given a 3% efficiency for the photoelectric effect, we can follow these steps:

### Step 1: Convert the wavelength from angstroms to meters
The wavelength given is \( 6600 \, \text{Å} \). We can convert this to meters:
\[ \lambda = 6600 \, \text{Å} = 6600 \times 10^{-10} \, \text{m} = 6.6 \times 10^{-7} \, \text{m} \]

### Step 2: Calculate the energy of one photon
The energy of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( h = 6.6 \times 10^{-34} \, \text{Js} \) (Planck's constant)
- \( c = 3 \times 10^{8} \, \text{m/s} \) (speed of light)
- \( \lambda = 6.6 \times 10^{-7} \, \text{m} \)

Substituting the values:
\[ E = \frac{(6.6 \times 10^{-34}) \times (3 \times 10^{8})}{6.6 \times 10^{-7}} \]
\[ E = \frac{19.8 \times 10^{-26}}{6.6 \times 10^{-7}} = 3 \times 10^{-19} \, \text{J} \]

### Step 3: Calculate the total energy emitted per second
The power of the light source is given as 24W. This means it emits 24 joules of energy per second.

### Step 4: Calculate the number of photons emitted per second
The number of photons emitted per second can be calculated using the formula:
\[ N = \frac{P}{E} \]
Where:
- \( P = 24 \, \text{W} = 24 \, \text{J/s} \)
- \( E = 3 \times 10^{-19} \, \text{J} \)

Substituting the values:
\[ N = \frac{24}{3 \times 10^{-19}} = 8 \times 10^{19} \, \text{photons/s} \]

### Step 5: Calculate the number of electrons emitted per second
Given the efficiency of the photoelectric effect is 3%, we can find the number of electrons emitted per second:
\[ \text{Number of electrons} = N \times \text{Efficiency} \]
Where:
- Efficiency = 0.03

Substituting the values:
\[ \text{Number of electrons} = 8 \times 10^{19} \times 0.03 = 2.4 \times 10^{18} \, \text{electrons/s} \]

### Final Answer
The number of electrons emitted per second by the source is \( 2.4 \times 10^{18} \, \text{electrons/s} \).

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