Radioactive decay & nuclear radiation

A radiation meter is placed at a distance d from a source of gamma radiation. The corrected count rate is 800 counts per second.

When the radiation meter is moved a further 10 cm from the source the corrected count rate is 600 counts per second.

What is d ?

A team of students uses 900 dice, each with n sides, to model the decay of a radioactive material. Each dice represents a single undecayed nucleus. A throw of the dice represents a constant time interval.

When the dice are thrown, those that show a 1 represent decayed nuclei and are removed. The students count the number N of ‘undecayed’ dice that remain. The procedure is repeated using the undecayed dice.

Figure 10 shows the students’ data.

Explain why N has been plotted on a logarithmic scale in Figure 10.

In this experiment, a decay constant λ can be defined that models the radioactive decay constant.

Determine λ. Go on to use your value for λ to show that n = 4 for the dice used in this experiment.

A typical radioactive source used in schools has an activity of 100 kBq. A radioactive source used in a hospital has an activity of 370 GBq.

State one safety measure when using a radioactive source in a school laboratory. Go on to discuss how this safety measure needs to be adapted for safe use of the hospital radioactive source.

X-rays are a form of ionising radiation.

A person has check-ups with a dentist every six months. The dentist only takes X-ray images when the person has reported a problem.

Suggest why.

Figure 4 shows a spark detector used to detect alpha particles.

The detector consists of a metal mesh placed 5.0 mm above a wire. A potential difference of 4000 V is applied between the mesh and the wire.

Molecules in the air between the mesh and the wire are ionised by an alpha particle and a spark is produced.

Figure 5 shows equipotentials between the mesh and the wire.

Figure 5 shows a dashed line between the mesh and the wire.

Sketch on Figure 6 a graph to show how the magnitude E of the electric field strength varies with the distance d from the mesh along this dashed line. No values are required on the E axis.

An alpha particle passes through the mesh. The alpha particle ionises an argon atom at P on Figure 5, releasing one electron. The electron and the argon ion have no kinetic energy at P. The electron then travels to the wire and the argon ion travels to the mesh.

Assume that the air has no effect on the motion of the electron or on the motion of the argon ion.

mass of argon ion = 6.64 × 10⁻²⁶ kg

In practice, the air does affect the motion of the electron and the motion of the argon ion.

Suggest how the presence of air between the mesh and the wire changes the ratio in Question 04.2. No numerical detail is required.

The alpha source in Figure 4 is moved to different heights h above the mesh.

Figure 7 shows how the number of sparks N produced in 10 minutes varies with h. No sparks are produced when the source is not present.

Student A suggests that the spark rate obeys an inverse-square law. Student B suggests that the spark rate decreases exponentially with h.

Determine whether either student is correct.

After radioactive waste is removed from a cooling pond, it is often stored in underground caves. This is to protect workers from the effects of

Radiation is used to measure the thickness of an aluminium sheet accurately. The thickness of the sheet is about 0.5 mm.

Which type of radiation is most appropriate for the measurement?

Which row is correct for α, β and γ radiation?

Which is not true for gamma radiation?

The diagram shows an area of 0.10 m² normal to a line connecting it to a point source of gamma radiation. The source emits photons uniformly in all directions. The area and the source are separated by a distance of 2.0 m.

The source emits 5000 gamma photons per second.

How many photons pass through the area every second?

Figure 1 shows apparatus used to investigate the inverse-square law for gamma radiation.

A sealed source that emits gamma radiation is held in a socket attached to clamp B. The vertical distance between the open end of the source and the bench is 138 mm. A radiation detector, positioned vertically above the source, is attached to clamp T.

A student is told not to move the stands closer together.

Describe a procedure for the student to find the value of d, the vertical distance between the open end of the source and the radiation detector.

In your answer, annotate Figure 1 to show how a set-square can be used in this procedure.

Before the source was brought into the room, a background count C_b was recorded.

With the source and detector in the positions shown in Figure 1, d = 530 mm. Separate counts C₁, C₂ and C₃ are recorded.

R_C is the mean count rate corrected for background radiation.

Show that when d = 530 mm, R_C is about 0.3 s⁻¹.

The apparatus is adjusted so that d = 380 mm. Counts are made that show R_C = 0.76 s⁻¹.

The student predicts that:

where k is a constant.

Explain whether the values of R_C in Questions 01.2 and 01.3 support the student’s prediction.

Describe a safe procedure to reduce d. Give a reason for your procedure.

The student determines R_C for further values of d. The values of d change by the same amount ∆ d between each measurement. Figure 2 shows these data.

Determine ∆ d.

Explain how the student could confirm whether Figure 2 supports the prediction:

No calculation is required.

When a gamma photon is detected by the detector, another photon cannot be detected for a time t_d called the dead time.

It can be shown that:

where R₁ is the measured count rate R₂ is the count rate when R₁ is corrected for dead time error.

The distance between the source and the detector is adjusted so that d is very small

On average, two of the gamma photons that enter the detector every second are not detected.

Calculate t_d for this detector.

A student says that if 100 gamma photons enter a detector in one second and t_d is 0.01 s, all the photons should be detected.

Explain, with reference to the nature of radioactive decay, why this idea is not correct.

A point source emits gamma radiation. The intensity I of the radiation is measured at different distances d from the source.

Which graph will show a straight line through the origin?

When a small radioactive source is placed in a cloud chamber, straight tracks about 4 cm long are observed. The same source is placed 10 cm from a Geiger tube and a count rate is detected. When a sheet of aluminium 5 mm thick is placed between the source and the Geiger tube the count rate falls to the background count rate.

Which types of radiation are emitted by the source?

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.

Suggest, with a reason, which type of radiation is likely to be the most appropriate for the sterilisation of metallic surgical instruments.

Explain why the public need not worry that irradiated surgical instruments become radioactive once sterilised.

A student detects the counts from a radioactive source using a G-M radiation detector as shown in Figure 10.

The student measures the count rate for three different distances d. Table 1 shows the count rate, in counts per minute, corrected for background for each of these distances.

Explain, with the aid of suitable calculations, why the data in Table 1 are not consistent with an inverse-square law. You may use the blank columns for your working.

State two possible reasons why the results do not follow the expected inverse-square law.

The results of the tests are shown in the table.

What is the radiation emitted by the source?