Nuclear Physics (DP IB Physics: HL)

Show that all nuclei have the same density.

A beam of neutrons is fired normally at a thin foil sheet made from tin. The beam has energy 75 MeV and the first diffraction minimum is observed at an angle of 15^o relative to the central bright fringe.

Calculate an estimate for the radius of the tin nucleus.

The tin () foil was replaced by thin aluminium () foil.

Deduce and explain the expected difference in the observations between the two experiments.

An isotope of tin has a half-life of 129 days. It undergoes beta-minus decay to a meta-stable isotope of antimony.

Calculate the percentage of the sample which will consist of antimony after 2 years.

Iodine-131  has a half-life of 8.02 days.

Calculate the decay constant of .

The initial activity of the sample of Iodine−131 is 6.5 × 10⁴ Bq.

Determine the activity after 16 days.

Determine the mass of the iodine−131 in the sample after 16 days.

Iodine−131 decays through a number of decay modes. Two of these are decay of 606 keV and gamma emission of 364 keV. The product of the  decay is . 

Sketch a nuclear energy level diagram to represent these decays. 

Ernest Rutherford was able to deduce a relationship for the size of the nucleus using the Rutherford scattering experiment shown below:

A radioisotope has a nuclear radius of 7.41 fm

Determine the nucleon number of the isotope.

A beam of high-energy neutrons is directed at the nucleus and a pattern is formed on a detector screen.

Explain the pattern which is observed.

The neutrons are accelerated to a speed of 2.88 × 10⁸ m s⁻¹.

Determine the angle of the first minimum.

The decay constant of the isotope is 9.72 × 10⁻¹⁰ yr⁻¹. The mass of a sample of this isotope is 600 g.

Determine the activity of the sample.

A nucleus of sodium−24 decays into a stable nucleus of magnesium−24. It decays by β^– emission followed by the emission of γ-radiation as the magnesium−24 nucleus de-excites into its ground state.

The sodium−24 nucleus can decay to one of three excited states of the magnesium−24 nucleus. This is shown in the diagram below:

The energies of the excited states are shown relative to the ground state.

Calculate the maximum possible speed of the emitted beta particle in MeV.

The excited magnesium nucleus de-excites through production of gamma radiation of discrete wavelengths.

Calculate the shortest wavelength of emitted radiation.

The graph shows the activity of a sample of sodium−24 with time.

Use the graph to calculate the decay constant of sodium−24.

The detector in this experiment measures 4% of the activity from the sample.

Determine the activity of sample after 27 hours from the start of the recording,

Americium-241 has a half-life of 432 years. A small sample is held in a school for use in experiments.

The teacher uses a Geiger-Müller counter to measure the count rate at close range. The relationship between activity and count rate is a ratio of 6:1. Over 5 minutes, the count is 13 600. 

Determine the activity of the sample.

Determine the activity of the americium sample after 748 years.

Americium−241 decays through a series of decays to uranium-233.

The energies from each decay path are recorded. 

Explain the differences between the energy profiles for the alpha decays and the beta decays.

The beta decay of protactinium−233 to uranium−233 has a half−life of 27 days. A sample of protactinium has an activity of 3879 Bq.

Determine the number of protactinium−233 nuclei in the sample.

In a scattering experiment, a metal foil of thickness 0.4 µm scatters 1 in 20 000 alpha particles through an angle greater than 90°.

Deviations from Rutherford scattering are observed when high-energy alpha particles are incident on nuclei.

Outline the incorrect assumption used in the Rutherford scattering formula and suggest an explanation for the observed deviations.

In a scattering experiment, alpha particles were directed at five different thin metallic foils, as shown in the table.

Metal	Symbol
Silver
Aluminium
Gold
Tin
Tungsten

Initially, all alpha particles have the same energy. This energy is gradually increased. 

Predict and explain the differences in deviations from Rutherford scattering that will be observed.

Outline why the particles must be accelerated to high energies in scattering experiments. 

Show that the decay constant is related to the half-life by the expression 

Uranium-238 has a half-life of 4.47 × 10⁹ years and decays to thorium-234. The thorium decays (by a series of further nuclear processes with short half-lives) to lead.

Assuming that a rock was originally entirely uranium and that at present, 1.5% of the nuclei are now lead, calculate the age of the rock. Give your answer in years to 2 significant figures.

The ionisation current I produced by α-particles emitted in the decay of radon can be measured experimentally. The logarithmic graph shows how current, ln I, varies with time, t.

Using the graph, determine the half-life of radon.

An electron beam of energy 1.3 × 10⁻¹⁰ J is used to study the nuclear radius of beryllium-9. The beam is directed from the left at a thin sample of beryllium-9. A detector is placed at an angle θ relative to the direction of the incident beam.

The radius of a beryllium-9 nucleus is 2.9 × 10⁻¹⁵ m. The beryllium-9 nuclei behave like a diffraction grating. 

Sketch the expected variation of electron intensity against the angle from the horizontal.

The isotope beryllium-10 is formed when a nucleus of deuterium collides with a nucleus of beryllium-9 . The radius of a deuterium nucleus is 1.5 fm.

[1]

The nucleus of beryllium-9 is replaced by a nucleus of gold-197.

Suggest the change, if any, to the following: 

Unstable uranium-238 has various nuclear decay modes to become stable thorium-234. The total amount of energy released when it decays is measured to be 210 keV. 

Outline, without calculation, the intermediate decay modes between the unstable uranium-238 to the stable thorium-234. 

A possible decay chain for uranium-238 is: 

Calculate the total amount of energy, in joules, carried away as gamma radiation in this decay chain. 

Deduce an alternative decay chain from unstable uranium-238 to stable thorium-234 which releases the same amount of energy in the form of gamma radiation as in part (b). 

Justify your answer with a calculation. 

The half-life of uranium-238 is so long in comparison to any of the isotopes in its decay chain that we can assume the number of lead-206 nuclei,  at any time is equal to the number of uranium-238 that have decayed. 

The number of uranium-238 nuclei  at time t is given by the equation: 

Where  is the number of uranium-238 nuclei at t = 0.

Show that the ratio of to  is given by:

Enriched uranium fuel is a mixture of the fissionable uranium-235 with the more naturally abundant uranium-238. Mixtures of radioactive nuclides such as this are very common in the nuclear power industry. 

Two samples of radioactive nuclides X and Y each have an activity of A₀ at t = 0. They are subsequently mixed together. 

The half-lives of X and Y are 16 and 8 years respectively. 

Show that the total activity of the mixture at time t = 48 years is equal to: