The frequency and intensity of a light source are both doubled. Consider the following statements
A. The saturation photocurrent remains almost the same
B. The maximum kinetic energy of the photoelectrons is double

Options

A. Both A and B are true.
B. A is true but B is false.
C. A is false but B is true
D. Both A and B are false.

Answer

To solve the problem, we need to analyze the two statements given in the question regarding the effects of doubling the frequency and intensity of a light source on the saturation photocurrent and the maximum kinetic energy of photoelectrons.

### Step-by-Step Solution:

1. **Understanding Photocurrent**:
- The saturation photocurrent is directly related to the number of photoelectrons emitted when light strikes a material. It is determined by the number of incident photons that have enough energy to eject electrons.

2. **Doubling Intensity and Frequency**:
- When the intensity of the light is doubled, it means that the energy per unit area per unit time is increased. However, this does not necessarily mean that the number of photons is doubled; instead, the energy of each photon is increased.
- When the frequency is doubled, the energy of each photon (given by \(E = h \nu\)) also doubles. Thus, while the energy per photon increases, the number of photons emitted may remain constant if the saturation photocurrent is to remain the same.

3. **Analyzing Statement A**:
- Since the number of photons (which contributes to the saturation photocurrent) does not change when we double the frequency (only the energy of each photon changes), the saturation photocurrent remains almost the same. Therefore, **Statement A is true**.

4. **Analyzing Statement B**:
- The maximum kinetic energy of the photoelectrons is given by the photoelectric equation:
\[ KE_{max} = h \nu - \phi \]
- If we double the frequency, we have:
\[ KE'_{max} = h (2\nu) - \phi = 2h \nu - \phi \]
- This can be rewritten as:
\[ KE'_{max} = 2(h \nu) - \phi \]
- The original kinetic energy was \(KE_{max} = h \nu - \phi\). Thus, the new kinetic energy is not simply double the original kinetic energy; it is increased by an additional amount equal to the original kinetic energy minus the work function. Therefore, **Statement B is false**.

5. **Conclusion**:
- Based on the analysis, we conclude that **Statement A is true** and **Statement B is false**.

### Final Answer:
- A is true but B is false.