7.1 Discrete Energy & Radioactivity

A radioactive nucleus  undergoes a beta−minus decay followed by an alpha decay to form a daughter nucleus .

Write a decay equation for this interaction and hence determine the values of A and Z.

Thorium, decays to an isotope of Radium (Ra) through a series of transformations. The particles emitted in successive transformations are:

Determine the resulting nuclide after these successive transformations. 

Through a combination of successive alpha and beta decays, the isotope of any original nucleus can be formed. 

Explain the simplest sequence of alpha and beta decays required to do this

A nucleus of Bohrium decays to Mendelevium by a sequence of three alpha particle emissions.

Determine the number of neutrons in a nucleus of

The table shows some of the isotopes of phosphorus and, where they are unstable, the type of decay.

Isotope
Type of decay			stable

State 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, .

Write a decay equation for this decay, finding the values of A and Z, and explain why each emission product occurs.

The radioactive isotope uranium−238 decays in a decay series to the stable lead−206. 

The half−life of is 4.5 × 10⁹ years, which is much larger than all the other half−lives of the decays in the series.

A rock sample, when formed originally, contained 6.0 × 10²² atoms of and no atoms. At any given time, most of the atoms are either or with a negligible number of atoms in other forms in the decay series.

Sketch on the axes below the variation of number of atoms and the number of atoms in the rock sample as they vary over a period of 1.0 × 10¹⁰ years from its formation. Label your graphs U and Pb.

A certain time, t, after its formation, the sample contained twice as many atoms as atoms. 

Show that the number of atoms in the rock sample at time t was 4.0 × 10²².

The ratio of the number of lead nuclei to the number of uranium nuclei at some time t is given by: 

λ is the decay constant and has a value of 1.54 × 10⁻¹⁰ years.

Calculate the time taken (in years) for there to be twice as many atoms as atoms.

Lead−214 is an unstable isotope of lead−206. It decays by emitting a  particle to form bismuth−214 (Bi) 

Bismuth is also unstable and has two decay modes: 

• Emitting an α particle to form thallium−210 (Tl) + energy
• Emitting a β particle to form polonium−214 (Po) + energy

Write decay equations for the decay chain of lead−214 to thallium−210 and to polonium−214. Comment on the nature of the energy released. 

The decay series of an isotope of thorium, ,  produces an isotope of radium, . This process involves four separate decays.

The first decay involves the emission of an alpha particle.

Write the decay equation for this process, including the symbol of the daughter product.

The first decay can be represented on an N-Z diagram as an arrow from point A to point B.

Three more decays occur before  is produced, denoted by “C” on the N-Z diagram.

Outline the possible sequence of decays which lead from point B to C.

Nuclei can be unstable for a number of reasons.

In terms of forces within the nucleus, explain why large nuclei emit alpha radiation.

 then decays four more times, shown below.

The first three decays result in the emission of an alpha particle each time. The fourth and final decay results in the emission of a beta-particle.

Calculate the nucleon number and atomic number of nuclide A.

A radioactive source is used to measure the thickness of paper. A Geiger counter is used to measure the count rate on the opposite side of the paper to the radioactive source.  The radioactive source used must be chosen carefully.

The arrangement below is used to maintain a constant 0.10 m thickness of aluminium sheets. Alpha, beta or gamma sources are available to be used.

Outline the most suitable radioactive source for this arrangement and explain why the other sources may not be appropriate.

The source used in part (b) has a half-life of 14 days and it has an initial count rate of 240 counts per minute when first used in the apparatus.

Giving your answer in weeks, calculate the length of time it takes for the Geiger counter to detect a count rate of 0.25 s^–1.

Once the source has reached an activity of 0.25 s^–1, it is replaced as the count rate of the source is comparable with that of background radiation.

State two natural sources of background radiation and two man-made sources of background radiation.

A sample’s count rate in counts per minute (cpm) is measured using a  ray detector. This data is plotted on a graph.

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The scientist wonders how the experiment in part (a) would have changed if the sample was twice the size.

Assuming the experiment from part (a) was repeated with a sample the exact same age but twice the mass, calculate the length of time it would have taken to reach a count rate of 22.5 cpm.

In reality the detector will measure a count rate of more than 5 cpm long after the length of time in part (b) has passed.

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The scientist can measure the count rate of the source but is unable to directly measure the activity of the source using their detector. Activity is the total number of particles emitted from the sample per unit time.

Explain why this is not possible.

Fluorescent tubes operate by exciting the electrons of mercury atoms.

The energy levels of a mercury atom are shown below (not to scale):

An electron is excited to n = 4. On the diagram, draw all the possible de-excitation routes from n = 4 to the ground state. 

State and explain which energy transition will emit the photon with the lowest frequency.

An unstable isotope of mercury, Hg-203, is tested for its radioactive emissions in a laboratory that has a background rate of 0.3 s^–1.

A source is placed a fixed distance from a Geiger-Muller tube. Various materials are placed in between the detector and the source while the count rate is recorded. The results are shown below.

State and explain what types of radiation are being emitted by the Hg-203 source.

A student notices that the count rate recorded actually increases when 0.5 mm thick paper was placed between the Geiger-Muller tube and the source.