State Examination Commission – Physics Higher Level, 2015
Question 7
X-rays have two important uses in medicine: imaging and radiation therapy.
Describe, with the aid of a labelled diagram of an X-ray tube, how X-rays are produced.
(14)
A potential difference of 50 kV is applied across an X-ray tube.
Calculate
(i) the maximum velocity of an electron in the tube
(ii) the minimum wavelength of the X-rays produced by the tube.
(18)
The large atoms found in bones (e.g. calcium and phosphorus) absorb X-ray photons. The small atoms found in soft
tissue (e.g. carbon and hydrogen) do not absorb X-ray photons. This is why bones cast shadows on an X-ray film.
The X-ray photons absorbed by large atoms can cause the photoelectric effect to occur.
What is the photoelectric effect?
Describe a laboratory experiment to demonstrate the photoelectric effect.
Albert Einstein received a Nobel Prize in 1921 for his explanation of the photoelectric effect.
Outline Einstein’s explanation of the photoelectric effect.
(24)
______________________________________________________________
Describe, with the aid of a labelled diagram of an X-ray tube, how X-rays are produced.
(14)
Electrons are emitted from the cathode by thermionic emission, accelerated across the evacuated tube by the
high voltage and strike the tungsten target producing X-rays.
A potential difference of 50 kV is applied across an X-ray tube.
Calculate
(i) the maximum velocity of an electron in the tube
Kinetic energy gained by the electron = Electrical potential energy lost
1
m v2 = eV
2
2 eV
v =
m
2×1.6×10−19 ×5×10 4
v =
9.1×10−31
8
−1
v = 1.4×10 ms
√
√
(ii) the minimum wavelength of the X-rays produced by the tube.
1
2
hf = eV
( = mv )
2
hc
= eV
λ
hc
λ =
eV
6.6×10−34×3.0×10 8
λ =
1.6×10−19×5.0×104
−11
λ = 2.5×10 m
(18)
C. Garvey 2015
The large atoms found in bones (e.g. calcium and phosphorus) absorb X-ray photons. The small atoms found in soft
tissue (e.g. carbon and hydrogen) do not absorb X-ray photons. This is why bones cast shadows on an X-ray film.
The X-ray photons absorbed by large atoms can cause the photoelectric effect to occur.
What is the photoelectric effect?
Textbook
Describe a laboratory experiment to demonstrate the photoelectric effect.
Textbook
Albert Einstein received a Nobel Prize in 1921 for his explanation of the photoelectric effect.
Outline Einstein’s explanation of the photoelectric effect.
(24)
Photons of radiation have a characteristic energy determined by their frequency. In the photoelectric effect, if an
electron absorbs the energy of one photon and has more energy than the work function (the minimum amount of energy
needed to eject an electron from the surface of the metal.), it is ejected from the material. If the photon energy is too
low, the electron is unable to escape the surface of the material.
Electrons can absorb energy from photons and they follow an "all or nothing" principle. All of the energy from one
photon is absorbed and used to liberate one electron from an atom. If the photon energy is absorbed, some of the energy
liberates the electron from the atom, and the remaining energy contributes to the electron's kinetic energy when freed.
hf = φ + ½mv2max ,
where h = Plancks constant, f = frequency of incident radiation, φ = work function of the metal and ½mv2max =
maximum kinetic energy of the emitted photoelectrons.