An X-ray beam transfers $400 \mathrm{J}$ of energy through an area of $5.0{ \mathrm{cm}}^2$ each second. Calculate its intensity in ${\mathrm{Wm}}^{-2}$.

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.

Quartz is an example of a piezo-electric material. The speed of sound in quartz is $5700{ \mathrm{ms}}^{-1}$.

(a) Calculate the wavelength of ultrasound waves of frequency $2.1\mathrm{MHz}$ in a quartz crystal.

Quartz is an example of a piezo-electric material. The speed of sound in quartz is $5700{ \mathrm{ms}}^{-1}$.

(b) If the crystal is to be used in an ultrasound transducer, its thickness must be half a wavelength. Calculate the thickness of the transducer.

Piezo-electric crystals have many applications other than in ultrasound scanning. For example, they are used in:

(a) Gas lighters (to produce a spark).