Download Medical Physics I: Basics of medical imaging and radiotherapy

Medical Physics I: Basics of medical imaging and radiotherapy
Prof. Dr. U. Oelfke – WS 2011/2012
Assignment I : Basic principles of an x-ray tube
1) Operation of an x-ray tube
Consider an x-ray tube in which the electrons are created by a heated cathode of lead or tungsten.
These electrons are then accelerated by an electric potential of Ua = 80kV (Distance cathode
– anode: 2 cm). Determine the following quantities for the operation of this x-ray tube by
employing the models discussed in class:
a) With what momentum will the electrons hit the anode? Is it sufficient to consider the
non-relativistic relationship between kinetic energy and velocity of the electron?
b) Determine the current density of the electrons at the anode and the tube current for a
focal spot size of 1 mm2 .
c) Determine the average velocity of electrons emitted from a cathode heated to a temperature
of 3000 K ?
2) x-ray energy spectrum
a) Determine the minimal wavelength λmin of an x-ray energy spectrum emitted by an x-ray
tube as a function of its accelerating voltage Ua , i.e., determine the relationship:
λmin [nm] = f (Ua [kV ]) ?
b) Calculate from the photon intensity spectrum
IE (E) ≡
dI
(E) = CZ(E0 − E)
dE
dI
the spectral intensity distribution per wavelength Iλ (λ) = dλ
(λ). Make a plot of Iλ (λ)
and determine the maximum of this function. How does Iλ (λ) change if one changes the
heating current at the cathode while keeping the electron accelerating voltage Ua constant
or vice versa if one changes the accelerating voltage while the heating of the cathode is
kept constant?
Assignment is due at 27. 10. 2011