Ultraviolet light of wavelength 66.26 nm and intensity `2 W//m^(2)` falls on potassium surface by which photoelectrons are ejected out. If only 0.1% of the incident photons produce photoelectrons, and surface area of metal surface is `4 m^(2)`, how many electrons are emitted per second?

Options

A. `2.67xx10^15`
B. `3xx10^15`
C. `3.33xx10^17`
D. `4.17xx10^16`

Answer

To solve the problem step by step, we will follow the outlined procedure to find the number of electrons emitted per second when ultraviolet light falls on the potassium surface.

### Step 1: Calculate the Energy of a Single Photon
The energy of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h = 6.626 \times 10^{-34} \, \text{J s} \) (Planck's constant)
- \( c = 3 \times 10^8 \, \text{m/s} \) (speed of light)
- \( \lambda = 66.26 \, \text{nm} = 66.26 \times 10^{-9} \, \text{m} \)

Substituting the values:
\[ E = \frac{(6.626 \times 10^{-34})(3 \times 10^8)}{66.26 \times 10^{-9}} \]

Calculating the energy:
\[ E = \frac{1.9878 \times 10^{-25}}{66.26 \times 10^{-9}} \approx 2.99 \times 10^{-18} \, \text{J} \]

### Step 2: Calculate the Number of Photons Incident per Second
The number of photons (\( N_p \)) falling on the surface per second can be calculated using the formula:
\[ N_p = \frac{I \cdot A}{E} \]
where:
- \( I = 2 \, \text{W/m}^2 \) (intensity)
- \( A = 4 \, \text{m}^2 \) (surface area)

Substituting the values:
\[ N_p = \frac{(2)(4)}{2.99 \times 10^{-18}} \]

Calculating the number of photons:
\[ N_p = \frac{8}{2.99 \times 10^{-18}} \approx 2.67 \times 10^{18} \, \text{photons/s} \]

### Step 3: Calculate the Number of Electrons Emitted
Given that only 0.1% of the incident photons produce photoelectrons, we can find the number of electrons emitted per second:
\[ N_e = 0.001 \times N_p \]

Substituting the value of \( N_p \):
\[ N_e = 0.001 \times 2.67 \times 10^{18} \approx 2.67 \times 10^{15} \, \text{electrons/s} \]

### Final Answer
The number of electrons emitted per second is approximately:
\[ \boxed{2.67 \times 10^{15}} \, \text{electrons/s} \]