When the energy of the incident radiation is increased by `20 %` , kinetic energy of the photoelectrons emitted from a metal surface increased from `0.5 eV to 0.8 eV`. The work function of the metal is

Options

A. `0.65eV`
B. `1.0eV`
C. `1.3eV`
D. `1.5eV`

Answer

To solve the problem, we need to determine the work function of the metal using the information provided about the kinetic energy of the emitted photoelectrons and the change in energy of the incident radiation.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The energy of the incident radiation (photon energy) can be expressed as:
\[ E = \text{Work Function} + \text{Kinetic Energy} \]
This can be written as:
\[ E = \phi + KE \]
where \( \phi \) is the work function and \( KE \) is the kinetic energy of the emitted photoelectrons.

2. **Setting Up the Equations**:
- In the first case, the kinetic energy of the photoelectrons is \( KE_1 = 0.5 \, \text{eV} \).
- Let the energy of the incident radiation in the first case be \( E_1 \).
- Therefore, we can write:
\[ E_1 = \phi + 0.5 \quad \text{(Equation 1)} \]

- In the second case, the energy of the incident radiation is increased by 20%. Thus, the new energy \( E_2 \) can be expressed as:
\[ E_2 = 1.2 E_1 \]
- The new kinetic energy of the photoelectrons is \( KE_2 = 0.8 \, \text{eV} \).
- Therefore, we can write:
\[ E_2 = \phi + 0.8 \quad \text{(Equation 2)} \]

3. **Substituting \( E_2 \) in Terms of \( E_1 \)**:
From Equation 2, substituting \( E_2 \):
\[ 1.2 E_1 = \phi + 0.8 \]

4. **Substituting \( E_1 \) from Equation 1**:
From Equation 1, we can express \( E_1 \):
\[ E_1 = \phi + 0.5 \]
Now substituting this into the equation for \( E_2 \):
\[ 1.2(\phi + 0.5) = \phi + 0.8 \]

5. **Expanding and Rearranging**:
Expanding the left side:
\[ 1.2\phi + 0.6 = \phi + 0.8 \]
Rearranging gives:
\[ 1.2\phi - \phi = 0.8 - 0.6 \]
\[ 0.2\phi = 0.2 \]

6. **Solving for the Work Function \( \phi \)**:
Dividing both sides by 0.2:
\[ \phi = 1 \, \text{eV} \]

### Final Answer:
The work function of the metal is \( \phi = 1 \, \text{eV} \).