To solve the problem, we will use Einstein's photoelectric equation, which relates the energy of the incident photons to the work function of the metal and the kinetic energy of the emitted electrons.
### Step-by-Step Solution:
1. **Understand the Given Data:**
- Maximum wavelength (\( \lambda_0 \)) that can produce the photoelectric effect = 200 nm
- Wavelength of incident radiation (\( \lambda \)) = 100 nm
2. **Convert Wavelengths to Meters:**
- \( \lambda_0 = 200 \, \text{nm} = 200 \times 10^{-9} \, \text{m} \)
- \( \lambda = 100 \, \text{nm} = 100 \times 10^{-9} \, \text{m} \)
3. **Calculate the Work Function (\( W_0 \)):**
- The work function \( W_0 \) can be calculated using the formula:
\[
W_0 = \frac{hc}{\lambda_0}
\]
- Where:
- \( h = 6.626 \times 10^{-34} \, \text{Js} \) (Planck's constant)
- \( c = 3 \times 10^8 \, \text{m/s} \) (speed of light)
- Substituting the values:
\[
W_0 = \frac{(6.626 \times 10^{-34} \, \text{Js})(3 \times 10^8 \, \text{m/s})}{200 \times 10^{-9} \, \text{m}}
\]
4. **Calculate the Energy of the Incident Photon (\( E \)):**
- The energy of the incident photon is given by:
\[
E = \frac{hc}{\lambda}
\]
- Substituting the values:
\[
E = \frac{(6.626 \times 10^{-34} \, \text{Js})(3 \times 10^8 \, \text{m/s})}{100 \times 10^{-9} \, \text{m}}
\]
5. **Calculate the Maximum Kinetic Energy (\( KE_{max} \)):**
- Using Einstein's photoelectric equation:
\[
KE_{max} = E - W_0
\]
- Substitute the values calculated for \( E \) and \( W_0 \).
6. **Convert Kinetic Energy to Electron Volts:**
- Since the answer is required in electron volts (eV), we convert Joules to eV using the conversion factor \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \).
7. **Final Calculation:**
- After performing the calculations, we find that the maximum kinetic energy acquired by the electron due to radiation of wavelength 100 nm is approximately \( 6.19 \, \text{eV} \).
### Summary:
The maximum kinetic energy acquired by the electron is approximately \( 6.2 \, \text{eV} \).
