Energy required to stop the ejection of electrons from Cu plate is 0.24eV. Calculate the work function when radiations of `lamda=253.7nm` strikes the plate.

Answer

To solve the problem, we need to calculate the work function of the copper plate when it is struck by radiation of wavelength \( \lambda = 253.7 \, \text{nm} \). The energy required to stop the ejection of electrons (the kinetic energy of the ejected electrons) is given as \( 0.24 \, \text{eV} \).

### Step-by-Step Solution:

1. **Convert the Wavelength to Meters**:
\[ \lambda = 253.7 \, \text{nm} = 253.7 \times 10^{-9} \, \text{m} \]

**Hint**: Remember that \( 1 \, \text{nm} = 10^{-9} \, \text{m} \).

2. **Calculate the Energy of the Incident Radiation**:
The energy \( E \) of the radiation 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:
\[ E = \frac{(6.63 \times 10^{-34} \, \text{J s}) \times (3 \times 10^8 \, \text{m/s})}{253.7 \times 10^{-9} \, \text{m}} \]

Calculating this gives:
\[ E \approx 7.83 \times 10^{-19} \, \text{J} \]

**Hint**: Make sure to keep track of units when substituting values into the formula.

3. **Convert Energy from Joules to Electron Volts**:
To convert the energy from Joules to electron volts, use the conversion factor \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \):
\[ E \approx \frac{7.83 \times 10^{-19} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 4.89 \, \text{eV} \]

**Hint**: Always remember to use the conversion factor correctly to avoid calculation errors.

4. **Calculate the Work Function**:
The work function \( \phi \) can be calculated using the equation:
\[ E = \phi + KE \]
where \( KE \) is the kinetic energy of the ejected electrons. Rearranging gives:
\[ \phi = E - KE \]
Substituting the values:
\[ \phi = 4.89 \, \text{eV} - 0.24 \, \text{eV} = 4.65 \, \text{eV} \]

**Hint**: Ensure that you are subtracting the kinetic energy from the total energy correctly.

### Final Answer:
The work function of the copper plate is approximately \( 4.65 \, \text{eV} \).