2.1 Atomic Structure & Decay Equations

A muon and an anti–muon annihilate leading to the emission of two photons.

Using your answer to part (a): 

(i)         Deduce the type of electromagnetic radiation emitted after the annihilation. 

(ii)        Explain why this is the longest possible wavelength of the photons produced.

Recombining the photons can produce a muon and an anti–muon in a process called pair production. Alternatively, one of the photons could spontaneously convert into an electron and positron.

In 1995, scientists at CERN created, for the first time, anti–atoms of hydrogen. Each of these consisted of a positron in orbit around an antiproton. Each anti–atom produced survived for only around forty nanoseconds.

Figure 1 shows a graph of neutron number N plotted against proton number Z for stable nuclei.

The solid line indicates where N = Z.

In terms of fundamental forces, suggest why stable nuclei of higher nucleon number have a greater numbers of neutrons than protons.

All nuclei have approximately the same density.

A proton travelling at a moderate velocity is fired at a stationary proton. It stops momentarily at a very short distance from the stationary proton and then deflects in the opposite direction.

 A proton travelling at a high velocity is then fired at the stationary proton. It also stops momentarily at a very short distance from the stationary proton but does not deflect.

Table 1 shows some of the isotopes of phosphorus and, where they are unstable, the type of decay.

Table 1

Isotope
Type of decay			stable

Predict whether the isotope   is stable or not. If not, determine, with a reason, the type of decay it experiences.

The isotope of phosphorus decays into an isotope of silicon.

In one instance, one of the unstable isotopes of phosphorus decays and is then immediately bombarded by electrons. This leads to the ionisation of the decay product. 

The specific charge of the ionised decay product is found to be 5.835 × 10⁶ C kg^–1 and it has a negative charge of 3.2 × 10^–19 C.

Calculate the percentage of the total mass of the ion in part (c) that is accounted for by the mass of its neutrons.

Under certain circumstances, it is possible for a pair of gamma ray photons to be created from a collision of an electron and positron.

Compare the mass, charge and rest mass energy of an electron and a positron. 

Calculate the minimum energy of each gamma ray photon in joules.

Calculate the wavelength of the gamma ray photons.

Describe the role of the strong nuclear force in keeping the nucleus stable.  

Describe how the strong nuclear force between a pair of nucleons varies with the separation of the nucleons, quoting appropriate values for separation.  

An unstable nucleus plutonium 239 () decays into an isotope of Uranium, U, by emitting an alpha particle.

The α particle is emitted from a stationary   nucleus at a speed of 4.5 × 10⁶ m s^–1.

Give your answer to an appropriate number of significant figures.

Explain the process of pair production.

Muons and antimuons are heavier versions of the electron and positron.

Give your answer to an appropriate number of significant figures.

Calculate the frequency and wavelength of the gamma ray photon required to create a muon-antimuon pair.  

A photon of slightly lower frequency than that calculated in part (c) does not convert into a muon-antimuon pair.

An unstable isotope of neodymium–144 () decays by emitting an α particle.

Determine the ratio  

An atom of  is instead ionised by the addition of three orbiting electrons.

State the constituents of the ion that have           

• A zero charge per unit mass ratio

• The smallest charge per unit mass ratio

• The largest charge per unit mass ratio

Calculate the percentage of the total mass of the ion that is accounted for by the mass of its electrons.