To solve the problem, we need to analyze the relationship between the stopping potential and the maximum kinetic energy of photoelectrons when ultraviolet light and X-rays are incident on a photocell.
### Step-by-Step Solution:
1. **Understanding the Photoelectric Effect**:
- When light (or any electromagnetic radiation) strikes a photocell, it can eject electrons. The energy of the incoming photons is converted into kinetic energy of the emitted electrons.
- The maximum kinetic energy (K_max) of the emitted electrons can be expressed as:
\[
K_{\text{max}} = E - W
\]
where \(E\) is the energy of the incoming photon and \(W\) is the work function of the material.
2. **Energy of Photons**:
- The energy of a photon is given by:
\[
E = \frac{hc}{\lambda}
\]
where \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength of the light.
- For ultraviolet light, the wavelength is in the range of \(10^{-7} \, \text{m}\) to \(10^{-8} \, \text{m}\).
- For X-rays, the wavelength is in the range of \(10^{-8} \, \text{m}\) to \(10^{-12} \, \text{m}\).
3. **Comparing Wavelengths**:
- Since the wavelength of X-rays is shorter than that of ultraviolet light, the energy of X-ray photons is greater than that of ultraviolet photons.
- Therefore, we can conclude:
\[
E_{\text{X-ray}} > E_{\text{UV}}
\]
4. **Maximum Kinetic Energy Comparison**:
- Since the work function \(W\) remains constant for the same material, we can compare the maximum kinetic energies:
\[
K_{\text{max, X-ray}} = E_{\text{X-ray}} - W > E_{\text{UV}} - W = K_{\text{max, UV}}
\]
- This implies:
\[
K_{\text{max, X-ray}} > K_{\text{max, UV}}
\]
5. **Stopping Potential**:
- The stopping potential \(V_0\) is related to the maximum kinetic energy by:
\[
K_{\text{max}} = eV_0
\]
where \(e\) is the charge of an electron.
- Since we established that \(K_{\text{max, X-ray}} > K_{\text{max, UV}}\), it follows that:
\[
V_{0, \text{X-ray}} > V_{0, \text{UV}}
\]
6. **Conclusion**:
- Both the maximum kinetic energy and the stopping potential increase when X-rays are incident on the photocell compared to ultraviolet light.
### Final Answer:
Both the maximum kinetic energy and the stopping potential increase when X-rays are incident on the photocell compared to ultraviolet light.
