IB Physics SL Radioactive Decay

Review IB Physics radioactive decay through isotopes, binding energy, mass defect, decay equations, half-life graphs, background count and nuclear stability.

Exam points

calculate binding energy, mass defect or Q-value using E=mc^2 and nuclear masses
write alpha, beta or gamma decay equations including neutrino and antineutrino symbols
correct for background count rate and use half-life or decay constant to find activity

Covered syllabus points

E.3.1—Isotopes E.3.2—Binding energy and mass defect E.3.3—Binding energy curve E.3.4—Mass-energy equivalence E.3.5—Strong nuclear force E.3.6—Random radioactive decay E.3.7—Decay nuclear changes E.3.8—Decay equations E.3.9—Neutrinos and antineutrinos E.3.10—Radiation penetration and ionization E.3.11—Activity, count rate and half-life E.3.12—Half-life changes E.3.13—Background radiation

[Maximum number: 8]

This section consists of three questions: B1, B2 and B3.

(a)

The isotope tritium (hydrogen-3) has a radioactive half-life of 12 days.

[ 2 ]

(i)

State what is meant by the term isotope.

[ 1 ]

(ii)

Define radioactive half-life.

[ 1 ]

(b)

Tritium may be produced by bombarding a nucleus of the isotope lithium-7 with a high-energy neutron. The reaction equation for this interaction is

{ }_{3}^{7} \mathrm{Li}+{ }_{0}^{1} \mathrm{n} \rightarrow{ }_{1}^{3} \mathrm{H}+{ }_{Z}^{4} \mathrm{X}+{ }_{0}^{1} \mathrm{n} .

[ 2 ]

(i)

Use the following data to show that the minimum energy that a neutron must have to initiate the reaction in (b)(i) is about 2.5 MeV .

\begin{array}{ll} \text { Rest mass of lithium-7 nucleus } & =7.0160 \mathrm{u} \\ \text { Rest mass of tritium nucleus } & =3.0161 \mathrm{u} \\ \text { Rest mass of X nucleus } & =4.0026 \mathrm{u} \end{array}

[ 2 ]

(mass difference $=) 7.0160-[3.0161+4.0026]=(-) 2.7 \times 10^{-3} \mathrm{u}$ ; ( energy required $=)(-) 2.7 \times 10^{-3} \times 931.5$ or 2.5151 MeV ; ( $\approx 2.5 \mathrm{MeV}$ )

Marking guidance:

Allow unit conversions via mass and $m c^{2}$ .

(c)

A nucleus of tritium decays to a nucleus of helium-3. Identify the particles X and Y in the nuclear reaction equation for this decay.

{ }_{1}^{3} \mathrm{H} \rightarrow{ }_{2}^{3} \mathrm{He}+\mathrm{X}+\mathrm{Y}

X:
Y:

[ 2 ]

$\beta^{-}$ or ${ }_{-1}^{0} \mathrm{e}$ or $\mathrm{e}^{-}$ or electron or beta particle;
$\bar{v}$ or ${ }_{0}^{0} \bar{v}$ or antineutrino;

Marking guidance:

Allow answers in either order.

(d)

A sample of tritium has an activity of $8.0 \times 10^{4} \mathrm{~Bq}$ at time t=0. The half-life of tritium is 12 days.

[ 2 ]

(i)

Using the axes below, construct a graph to show how the activity of the sample varies with time from t=0 to t=48 days.

[ 2 ]

[Maximum number: 10]

This question is in two parts. Part 1 is about renewable energy. Part 2 is about nuclear energy and radioactivity.

A small coastal community decides to use a wind farm consisting of five identical wind turbines to generate part of its energy. At the proposed site, the average wind speed is $8.5 \mathrm{~m} \mathrm{~s}^{-1}$ and the density of air is $1.3 \mathrm{~kg} \mathrm{~m}^{-3}$ . The maximum power required from the wind farm is 0.75 MW . Each turbine has an efficiency of 30 %.

(a)

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

[ 1 ]

(b)

On the axes, sketch a graph showing the variation of nucleon number with the binding energy per nucleon.

[ 2 ]

(c)

Explain, with reference to your graph, why energy is released during fission of U-235.

[ 3 ]

(d)

U-235 $\left({ }_{92}^{235} \mathrm{U}\right)$ can undergo alpha decay to form an isotope of thorium (Th).

[ 4 ]

(i)

State the nuclear equation for this decay.

[ 1 ]

${ }_{92}^{235} \mathrm{U} \rightarrow{ }_{90}^{231} \mathrm{Th}+{ }_{2}^{4} \alpha$ ; (allow He for $\alpha$ ; treat charge indications as neutral)

(ii)

Define the term radioactive half-life.

[ 1 ]

(iii)

A sample of rock contains a mass of 5.6 mg of U-235 at the present day.

The half-life of U-235 is $7.0 \times 10^{8}$ years. Calculate the initial mass of the U-235 if the rock sample was formed $2.1 \times 10^{9}$ years ago.

[ 2 ]

All question bank results loaded

Covered syllabus points

E.3 Radioactive decay question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (c)

Question (d)

Question (i)

E.3 Radioactive decay question 2

Question (a)

Question (b)

Question (c)

Question (d)

Question (i)

Question (ii)

Question (iii)