Nuclear Physics

Define activity of a radioactive sample.

Explain why the variation with time of the activity of a radioactive sample is exponential in nature.

Determine the decay constant, in $\text{min}^{-1}$, of the radioactive isotope.

decay constant = ______ $\text{min}^{-1}$

Use your answer in (c)(i) to determine the half-life, in min, of the radioactive isotope.

half-life = ______ $\text{min}$

On Fig. 9.1, sketch the variation of the activity $A$ of the sample with $t$ for values of $t$ between $t = 0$ and $t = 24\ \text{min}$.

Radioactive decay is a spontaneous process.

State the meaning, in this context, of the term spontaneous.

Complete Table 10.1 to give expressions, in terms of either or both of $A$ and $T$, for the quantities indicated for each of the samples.

Table 10.1

Determine, in terms of $T$, the time at which the two samples will have equal activities.

time = ______ $T$

A radiation detector is placed near to one of the samples in (b).

Explain why the count rate measured by the detector is less than the activity of the sample.

Define activity of a radioactive sample.

Explain why the variation with time of the activity of a radioactive sample is exponential in nature.

Determine the decay constant, in $\text{min}^{-1}$, of the radioactive isotope.

decay constant = ______ $\text{min}^{-1}$

Use your answer in (c)(i) to determine the half-life, in min, of the radioactive isotope.

half-life = ______ $\text{min}$

On Fig. 9.1, sketch the variation of the activity $A$ of the sample with $t$ for values of $t$ between $t = 0$ and $t = 24\ \text{min}$.

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

Determine the number of neutrons produced in this fission reaction.

number = ______

Data for the binding energies per nucleon for this fission reaction are given in Table 8.1.

Table 8.1

Calculate the energy released, in MeV, from the fission of one nucleus of uranium-235.

energy = ______ $\text{MeV}$

The isotope xenon-142 is unstable. The isotope xenon-132 is stable.

Suggest a reason why xenon-142 is unstable.

Xenon-142 decays into the isotope caesium-142.

A sample initially contains only nuclei of xenon-142. After a time equal to $6.0 \text{ s}$, the ratio

is equal to 31.

Calculate the half-life of xenon-142. Show your working.

half-life = ______ $\text{s}$

Define half-life of a radioactive isotope.

State the name of the quantity represented by the magnitude of the gradient of line X in Fig. 9.1.

State three conclusions about X or Y that may be drawn from Fig. 9.1. The conclusions may be qualitative or quantitative. Use the space below for any working that you need.

The mass of radioactive isotope X in the sample in (b) is $7.3 \times 10^{-4}\ \text{kg}$ at time $t = 0$.

Determine the nucleon number of isotope X.

nucleon number = ______

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

the mass defect $\Delta m$, in $\text{kg}$

$\Delta m$ = ______ $\text{kg}$

the binding energy

binding energy = ______ $\text{J}$

the binding energy per nucleon.

binding energy per nucleon = ______ $\text{J}$

On Fig. 9.1, sketch the variation with nucleon number $A$ of binding energy per nucleon for values of $A$ from $1$ to $250$.

On your line in Fig. 9.1, draw an X to show the approximate position of polonium-212.

Polonium-212 is radioactive and undergoes alpha-decay.

Suggest and explain, with reference to Fig. 9.1, why the alpha-decay of polonium-212 results in a release of energy.

Define half-life of a radioactive isotope.

State the name of the quantity represented by the magnitude of the gradient of line X in Fig. 9.1.

State three conclusions about X or Y that may be drawn from Fig. 9.1. The conclusions may be qualitative or quantitative. Use the space below for any working that you need.

The mass of radioactive isotope X in the sample in (b) is $7.3 \times 10^{-4}\ \text{kg}$ at time $t = 0$.

Determine the nucleon number of isotope X.

nucleon number = ______

State the name of the beta-plus particle.

Show that the decay constant of fluorine-18 is $1.05 \times 10^{-4}\ \text{s}^{-1}$.

Determine the activity of $2.1 \times 10^{-12}\ \text{kg}$ of fluorine-18.

activity = ______ $\text{Bq}$

Describe how the interaction of a $\beta^+$ particle with an electron in the body enables the formation of an image.

Suggest why 110 minutes is a suitable half-life for a nuclide used as a tracer in medical diagnosis.

State what is meant by random.

State what is meant by spontaneous.

State one piece of evidence for the random nature of decay.

Describe the differences between nuclear fission and nuclear fusion.

Explain, with reference to the variation of binding energy per nucleon with nucleon number, why the processes of nuclear fission and nuclear fusion both result in a release of energy.

Complete the equation to show the decay of plutonium-238.

Calculate the initial number $N_o$ of nuclei of plutonium-238 in the power source.

$N_o$ = ______

Determine the initial activity of the source. Give a unit with your answer.

activity = ______ unit ______

Use your answer in (b)(ii) to determine the initial power output from the source due to the decay of plutonium-238.

power output = ______ $\text{W}$

The space probe will continue to function until the power output from the plutonium in the source decreases to $65.3\%$ of its initial value.

Calculate the time, in years, for which the space probe will function.

time = ______ $\text{years}$

An alternative power source uses energy generated from the radioactive decay of polonium-210. This isotope has a half-life of $0.378\ \text{years}$. The mass of the isotope needed for the same initial power output as in (b) is $3.37\ \text{g}$.

Suggest one advantage and one disadvantage of using polonium-210 as the source of energy.

advantage .................................................................................................................................

disadvantage ............................................................................................................................