Explanation:

To understand why option B is the wrong statement, let's first understand the concept of X-rays generated from an X-ray tube.

An X-ray tube consists of a cathode and an anode. When a high voltage is applied across these two electrodes, electrons are emitted from the cathode and accelerated towards the anode. The high-speed electrons collide with the target material (anode) and produce X-rays through two different processes: characteristic X-ray production and bremsstrahlung (continuous) X-ray production.

Characteristic X-rays:
- When high-speed electrons collide with the target material (anode), they can eject inner-shell electrons from the target atoms.
- When these inner-shell electrons are ejected, outer-shell electrons fill the vacancies, and in the process, they release energy in the form of X-rays.
- The energy of these characteristic X-rays depends on the difference in energy between the outer and inner electron shells involved in the transition.
- The wavelength of characteristic X-rays is inversely proportional to their energy, according to the equation λ = hc/E, where λ is the wavelength, h is Planck's constant, c is the speed of light, and E is the energy of the X-rays.
- Therefore, the wavelength of characteristic X-rays decreases as the energy (or frequency) increases.

Continuous X-rays (Bremsstrahlung):
- When high-speed electrons pass near the nucleus of the target atoms, they are deflected due to the electrical interaction with the positively charged nucleus.
- This deflection causes the electrons to lose energy, which is emitted in the form of X-rays.
- The energy (and therefore the wavelength) of these bremsstrahlung X-rays depends on the energy of the electrons before the deflection.
- As the energy of the electrons increases, the energy (and hence the wavelength) of the bremsstrahlung X-rays also increases.

Now, let's analyze the statements:
a) Wavelength of characteristic X-rays decreases when the atomic number of the target increases.
- This statement is correct. As mentioned earlier, the energy of characteristic X-rays depends on the energy difference between the outer and inner electron shells involved in the transition. Since the energy difference is related to the atomic number (Z) of the target material, the wavelength of characteristic X-rays decreases as the atomic number of the target material increases.

b) Cut-off wavelength of the continuous X-rays depends on the atomic number of the target.
- This statement is incorrect. The cut-off wavelength of continuous X-rays (bremsstrahlung X-rays) depends on the energy of the electrons before the deflection, not on the atomic number of the target material. The cut-off wavelength is determined by the maximum energy of the electrons, not the target material.

c) Intensity of the characteristic X-rays depends on the electrical power given to the X-ray tube.
- This statement is correct. The intensity of characteristic X-rays depends on the number of collisions between high-speed electrons and target atoms. The number of collisions (and hence the intensity of X-rays) is directly proportional to the electrical power given to the X-ray tube.

d) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube.
- This statement is correct. As mentioned earlier, the energy (and therefore the wavelength) of continuous X