Medical physics：練習題

What is the primary function of a Computed Tomography (CT) scan in medical imaging compared to a standard X-ray?

The picture shows the variation of the intensity \(I\) of a parallel beam of X-rays as it passes through a specific material of thickness \(x\). Based on the data in the graph, what is the linear attenuation coefficient \(\mu\) of the material?

In a PET scanner, a positron and an electron annihilate to produce two gamma-ray photons of equal energy. Given that the rest mass of an electron is \(9.11 \times 10^{-31}\text{ kg}\), what is the frequency of each produced photon?

In Positron Emission Tomography (PET) scanning, what is the origin of the gamma-ray photons detected by the scanner?

The acoustic impedance of soft tissue is \(1.63 \times 10^6\text{ kg m}^{-2}\text{ s}^{-1}\) and the acoustic impedance of bone is \(6.12 \times 10^6\text{ kg m}^{-2}\text{ s}^{-1}\). What is the intensity reflection coefficient \(\alpha\) for an ultrasound wave traveling from soft tissue to bone?

A specific ultrasound scan uses a frequency of \(5.0 \text{ MHz}\). The acoustic impedance of a certain soft tissue is \(1.63 \times 10^6 \text{ kg m}^{-2} \text{s}^{-1}\) and its density is \(1040 \text{ kg m}^{-3}\). Determine the wavelength of the ultrasound waves in this tissue.

A positron and an electron annihilate to produce two photons. Calculate the minimum total energy, in \(\text{MeV}\), of the two photons produced. Use the mass of an electron \(m_e = 9.11 \times 10^{-31} \text{ kg}\) and the conversion factor \(1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}\).

Calculate the minimum wavelength of X-rays produced when electrons are accelerated through a potential difference of \(60.0 \text{ kV}\).

(a) X-rays are produced when high-speed electrons decelerate upon hitting a metal target. Explain why there is a minimum wavelength for the X-rays produced for a given accelerating potential difference.
(b) Calculate the minimum wavelength of X-rays produced when the accelerating potential difference is \(85.0\text{ kV}\).
(c) State the effect on the minimum wavelength if the accelerating potential difference is increased.

(a) Define the half-value layer (HVL) for a material used to attenuate X-rays.
(b) Show that the linear attenuation coefficient \(\mu\) is related to the half-value layer \(x_{1/2}\) by the equation \(\mu = \frac{\ln 2}{x_{1/2}}\).
(c) A parallel beam of X-rays is filtered by a lead shield. The HVL of lead for this beam is \(0.40\text{ mm}\). Calculate the percentage of the incident intensity that is transmitted through a lead sheet of thickness \(1.8\text{ mm}\).