Nuclear instability and the N-Z graph

241Am decays to one of two excited states of 237 Np by emitting an alpha particle. 95 93 The excited 237 93 Np nucleus then decays with the emission of a gamma photon.

What is the energy of the emitted gamma photon that has the shortest wavelength?

Which decay produces an atom with electrons in excited states?

The graph shows a plot of neutron number N against proton number Z for the known atomic nuclei.

The nuclide 115 45Rh is likely to decay by

Uranium-238 absorbs a neutron in the first stage in a series of nuclear reactions that end in a nucleus Z.

238

How many neutrons does Z have?

Fission and fusion are two processes that can result in the transfer of binding energy from nuclei.

State what is meant by the binding energy of a nucleus.

Calculate, in MeV, the binding energy for a nucleus of iron 5626Fe.

Figure 10 shows a graph of average binding energy per nucleon against nucleon number for common nuclides.

The nuclide labelled X in Figure 10 undergoes fission.

Annotate Figure 10 with F₁ and F₂ to show one possible pair of nuclides resulting from the fission of X.

Figure 11 shows a graph of N against Z for stable nuclides.

Deduce the likely initial mode of decay of F₁ and F₂. Refer to Figure 11 in your answer.

Section B

Each of Questions 07 to 31 is followed by four responses, A, B, C and D.

For each question select the best response.

Which provides evidence for the existence of energy levels in nuclei?

27Mg can decay by beta minus emission to one of two possible excited states of 27 Al. 12 13 Both excited states decay by the emission of a gamma photon directly to the ground state.

The diagram shows the energy levels and two routes for the beta decay.

One route results in the emission of a gamma photon with a higher frequency than the other photon.

What is the maximum possible kinetic energy for the beta particle emitted in this route?

A deuterium nucleus and a tritium nucleus fuse together to form a helium nucleus and a particle X. The equation for this process is:

2 3 4

What is X ?

Figure 1 shows a sealed radioactive source used in schools and colleges.

State two safety procedures to reduce risk when using this type of source.

Safety procedure 1

Safety procedure 2

226²²⁶Ra A sealed source contains radium- (₈₈).

²²⁶₈₈Ra decays by emitting and ^– particles to produce²⁰⁶₈₂Pb which is stable.

Figure 2 is a graph of neutron number N against proton number Z, showing the different ways that²²⁶₈₈Ra can decay into²⁰⁶₈₂Pb.

Points A to M represent all the unstable nuclei that may be formed as²²⁶₈₈Ra decays into²⁰⁶₈₂Pb.

Determine the number of routes by which B can change into K.

Identify which of the nuclei A to M are common to all the possible ways that²²⁶₈₈Ra

The sealed source emits γ radiation in addition to and ^– particles. A student uses the sealed source to investigate the inverse-square law for γ radiation. The student begins by making measurements to find the count rate A_b for the background radiation.

State and explain procedures

to eliminate systematic error in the measurements used to find A_b

to reduce the percentage uncertainty in A_b.

Figure 3 shows an aluminium absorber placed between the sealed source and a radiation detector. This is to make sure that only γ radiation from the source reaches the detector.

The sealed source emits:

• particles with energy E_k between 3.8 MeV and 7.8 MeV

• ^– particles with energy E_k between zero and 5.5 MeV.

Figure 4 shows how the range of ^– particles in aluminium depends on E_k.

Deduce the minimum thickness of the aluminium absorber that should be used in the experiment.

Ionisation takes place inside the detector. The effective distance travelled by radiation from the source is (d + e). The distance e, shown in Figure 5, cannot be measured directly.

From the inverse-square law for radiation, it can be shown that

where A is the count rate, corrected for background radiation k is a constant. The student plots the graph of d against shown in Figure 6.

Deduce k using Figure 6. Explain your reasoning. Give a suitable unit for your result.

Determine e using Figure 6.

A nucleus of polonium Po may decay to the stable isotope of lead²⁰⁸₈₂Pb through a chain of emissions following the sequence ^{– –} .

Figure 13 shows the position of the isotope²⁰⁸₈₂Pb on a grid of neutron number N against proton number Z.

Draw four arrows on Figure 13 to show the sequence of changes to N and Z that occur as the polonium nucleus is transformed into²⁰⁸₈₂Pb.

A nucleus of the stable isotope²⁰⁸₈₂Pb has more neutrons than protons.

Explain why there is this imbalance between proton and neutron numbers by referring to the forces that operate within the nucleus. Your explanation should include the range of the forces and which particles are affected by the forces.

Many, but not all, isotopes of lead are stable. For example,²⁰⁵₈₂Pb decays by electron capture to become an isotope of thallium, Tl.

Write the equation to represent this decay, including the isotope of thallium produced.

The thallium nucleus is formed in an excited state. Electromagnetic radiation is emitted from the thallium atom following its formation.

Explain the origin and location of two sources of this radiation.

Other nuclides also emit electromagnetic radiation.

Explain why the metastable form of the isotope of technetium⁹⁹₄₃Tc is a radioactive source suitable for use in medical diagnosis.

Section B

Each of Questions 08 to 32 is followed by four responses, A, B, C and D.

For each question select the best response.

Calculate the binding energy, in MeV, of a nucleus of⁵⁹₂₇ Co.

A nucleus of iron Fe-59 decays into a stable nucleus of cobalt Co-59. It decays by ⁻ emission followed by the emission of -radiation as the Co-59 nucleus de-excites into its ground state.

The total energy released when the Fe-59 nucleus decays is 2.52 × 10⁻¹³ J.

The Fe-59 nucleus can decay to one of three excited states of the cobalt-59 nucleus as shown in Figure 5. The energies of the excited states are shown relative to the ground state.

Calculate the maximum possible kinetic energy, in MeV, of the ⁻ particle emitted when the Fe-59 nucleus decays into an excited state that has energy above the ground state.

Following the production of excited states of⁵⁹₂₇ Co, -radiation of discrete wavelengths is emitted.

State the maximum number of discrete wavelengths that could be emitted.

Calculate the longest wavelength of the emitted -radiation.

longest wavelength = m 9