To solve the problem, we will use the concept of the photoelectric effect and the relationship between the energy of the incident light and the maximum kinetic energy of the emitted electrons.
### Step-by-Step Solution:
1. **Understanding the Photoelectric Effect Equation**:
The energy of the incident light (E) is given by the equation:
\[
E = \phi + K.E.
\]
where \( \phi \) is the work function of the metal and \( K.E. \) is the maximum kinetic energy of the emitted electrons.
2. **Calculating the Energy of Incident Light at 300 Å**:
The energy of the incident light can be calculated using the formula:
\[
E = \frac{12400}{\lambda}
\]
where \( E \) is in electron volts (eV) and \( \lambda \) is in angstroms (Å). For \( \lambda = 300 \, \text{Å} \):
\[
E = \frac{12400}{300} = 41.33 \, \text{eV}
\]
3. **Finding the Work Function (\( \phi \))**:
From the problem, we know that the maximum kinetic energy (\( K.E. \)) is 0.5 eV when the wavelength is 300 Å. Therefore:
\[
41.33 \, \text{eV} = \phi + 0.5 \, \text{eV}
\]
Rearranging gives:
\[
\phi = 41.33 \, \text{eV} - 0.5 \, \text{eV} = 40.83 \, \text{eV}
\]
4. **Calculating the Energy of Incident Light at 2000 Å**:
Now, we need to find the energy of the incident light when the wavelength is changed to 2000 Å:
\[
E = \frac{12400}{2000} = 6.2 \, \text{eV}
\]
5. **Comparing the Energy with the Work Function**:
We compare the energy of the incident light at 2000 Å with the work function:
- Work function \( \phi = 40.83 \, \text{eV} \)
- Energy at 2000 Å \( E = 6.2 \, \text{eV} \)
Since \( 6.2 \, \text{eV} < 40.83 \, \text{eV} \), the energy of the incident light is less than the work function.
6. **Conclusion**:
Since the energy of the incident light at 2000 Å is less than the work function, no photoelectric effect will occur. Therefore, the maximum kinetic energy of the emitted electrons will be:
\[
\text{Max K.E.} = 0 \, \text{eV}
\]
### Final Answer:
The maximum kinetic energy of emitted electrons when the wavelength is changed to 2000 Å will be 0 eV (no photoelectric effect occurs).
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