Which of the following statements are correct for an X-ray tube?

Options

A. On increasing potential difference between the filament and target, photon flux of X-rays increase.
B. On increasing potential difference between the filament and target, frequency of X-rays increases.
C. On increasing filament current, cut-off wavelength increases.
D. On increasing filament current, intensity of X-ray increases.

Explanation

To determine which statements are correct for an X-ray tube, we can analyze each statement based on the principles of how an X-ray tube operates.

### Step-by-step Solution:

1. **Understanding the X-ray Tube Structure**:
- An X-ray tube consists of a cathode (filament) and an anode (target material). The cathode emits electrons when heated, and these electrons are accelerated towards the anode by applying a high potential difference (voltage).

2. **Effect of Increasing Potential Difference**:
- When the potential difference between the filament (cathode) and the target (anode) is increased, the electrons gain more kinetic energy as they travel towards the anode. This results in higher energy collisions when they strike the target material.

3. **Photon Energy and Frequency**:
- The energy of the emitted X-rays is directly related to the kinetic energy of the electrons. Since energy (E) is related to frequency (ν) by the equation \( E = hν \) (where \( h \) is Planck's constant), an increase in electron kinetic energy leads to an increase in the frequency of the emitted X-rays.

4. **Cut-off Wavelength**:
- The cut-off wavelength (λ) is inversely related to the maximum energy of the emitted X-rays. As the energy increases, the cut-off wavelength decreases. However, if we are only increasing the filament current and not the potential difference, the cut-off wavelength remains constant.

5. **Intensity of X-rays**:
- The intensity of the X-ray beam is proportional to the number of photons produced. Increasing the filament current increases the number of electrons emitted, which in turn increases the number of X-ray photons produced. Therefore, increasing the filament current results in an increase in intensity.

6. **Photon Flux**:
- Photon flux refers to the number of photons emitted per unit time. This is influenced by the number of electrons hitting the target. If we only increase the potential difference without increasing the filament current, the photon flux does not necessarily increase.

### Summary of Statements:
- **Statement A**: "Photon flux of X-ray increases on increasing potential difference between the filament and target." (Incorrect)
- **Statement B**: "Frequency of X-ray increases on increasing potential difference." (Correct)
- **Statement C**: "Cut-off wavelength decreases on increasing filament current." (Incorrect)
- **Statement D**: "Intensity of X-ray increases on increasing filament current." (Correct)

### Correct Statements:
- B and D are correct.