(a)  Summarise the energy changes that take place in an X-ray tube.

(b) An X-ray tube is operated with a potential difference of $80 kV$ between the cathode and the tungsten anode. Calculate the kinetic energy (in electronvolts and joules) of an electron arriving at the anode. Estimate the impact speed of such an electron (assume that the electron is non-relativistic).

Charge on an electron $=1.6\times {10}^{-19 }C$

Mass of an electron $=9.1\times {10}^{-31} kg$

Determine the minimum wavelength of X-rays emitted from an X-ray tube operated at a voltage of $120\mathrm{kV}$.

Charge of an electron $=1.6\times {10}^{-19 }C$

Speed of light in vacuum $=3\times {10}^8 m/s$

3 Use the equation $I=I_0{\mathrm{e}}^{-\mu x}$ to show that the half thickness $x_{1/2}$ is related to the attenuation coefficient $\mu$ by:
$x_{1/2}=\frac{\ln 2}{\mu }$.

The data in Table, shows how the attenuation coefficient $\mu$ depends on the energy of the X-rays in bone and muscle. When making a diagnostic X-ray image, it is desirable that bone should be clearly distinguished from muscle. Use the data in Table, to explain why it would be best to use lower energy $\left(50\mathrm{keV}\right)$ X-rays for this purpose.

When low-energy X-rays are used, the attenuation coefficient $\mu$ is (roughly) proportional to the cube of the proton number$Z$ of the absorbing material. Use the data in Table to show that bone absorbs X-rays eight times as strongly as muscle.