IB Physics SL E.3 Radioactive Decay Question Bank

[Maximum number: 8]

(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 ]

[Maximum number: 7]

(a)

During electron capture, an atomic electron is captured by a proton in the nucleus. The stable nuclide thallium-205 $\left({ }_{81}^{205} \mathrm{Tl}\right)$ can be formed when an unstable lead (Pb) nuclide captures an electron.

Write down the equation to represent this decay.

\square \mathrm{Pb}+\square \mathrm{e}_{\mathrm{e}}

[ 2 ]

${}^{205}_{82}\mathrm{Pb}+{}^{0}_{-1}\mathrm{e}\rightarrow{}^{205}_{81}\mathrm{Tl}+{}^{0}_{0}\nu_e$ .

{}^{205}_{82}\mathrm{Pb}+{}^{0}_{-1}\mathrm{e}\rightarrow{}^{205}_{81}\mathrm{Tl}+{}^{0}_{0}\nu_e

(b)

The neutron number N and the proton number Z are not equal for the nuclide ${ }_{81}^{205} \mathrm{Tl}$ . Explain, with reference to the forces acting within the nucleus, the reason for this.

[ 2 ]

(c)

Thallium-205 $\left({ }_{81}^{205} \mathrm{Tl}\right)$ can also form from successive alpha ( $\alpha$ ) and beta-minus ( $\beta^{-}$ ) decays of an unstable nuclide. The decays follow the sequence $\alpha \beta^{-} \beta^{-} \alpha$ . The diagram shows the position of $\frac{205}{81} \mathrm{Tl}$ on a chart of neutron number against proton number.

Draw four arrows to show the sequence of changes to N and Z that occur as the ${ }_{81}^{205} \mathrm{Tl}$ forms from the unstable nuclide.

[ 3 ]

any $\alpha$ change correct

any $\beta$ change correct

diagram fully correct

Award [2 max] for a correct diagram without arrows drawn.

For MP1 accept a (-2, -2) line with direction indicated, drawn at any position in the graph.

For MP2 accept a (1, -1) line with direction indicated, drawn at any position in the graph.

Award [1] max for a correct diagram with all arrows in the opposite direction

[Maximum number: 1]

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

State what is meant by the term isotope.

[Maximum number: 1]

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 %.

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

[Maximum number: 2]

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} .

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}

(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 $m c^{2}$ .

[Maximum number: 2]

The neutron number N and the proton number Z are not equal for the nuclide ${ }_{81}^{205} \mathrm{Tl}$ . Explain, with reference to the forces acting within the nucleus, the reason for this.

[Maximum number: 2]

Radioactive decay is said to be "random" and "spontaneous". Outline what is meant by each of these terms.

Random:
Spontaneous:

[Maximum number: 3]

Thallium-205 $\left({ }_{81}^{205} \mathrm{Tl}\right)$ can also form from successive alpha ( $\alpha$ ) and beta-minus ( $\beta^{-}$ ) decays of an unstable nuclide. The decays follow the sequence $\alpha \beta^{-} \beta^{-} \alpha$ . The diagram shows the position of $\frac{205}{81} \mathrm{Tl}$ on a chart of neutron number against proton number.

Draw four arrows to show the sequence of changes to N and Z that occur as the ${ }_{81}^{205} \mathrm{Tl}$ forms from the unstable nuclide.

any $\alpha$ change correct

any $\beta$ change correct

diagram fully correct

Award [2 max] for a correct diagram without arrows drawn.

For MP1 accept a (-2, -2) line with direction indicated, drawn at any position in the graph.

For MP2 accept a (1, -1) line with direction indicated, drawn at any position in the graph.

Award [1] max for a correct diagram with all arrows in the opposite direction

[Maximum number: 2]

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:

$\beta^{-}$ 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.

[Maximum number: 1]

This question is in two parts. Part 1 is about kinematics and gravitation. Part 2 is about radioactivity.
Part 1 Kinematics and gravitation
A ball is released near the surface of the Moon at time t=0. The point of release is on a straight line between the centre of Earth and the centre of the Moon. The graph below shows the variation with time t of the displacement s of the ball from the point of release.

The nuclear equation for the decay of calcium-47 into scandium-47 $\left({ }_{21}^{47} \mathrm{Sc}\right)$ is given by

{ }_{20}^{47} \mathrm{Ca} \rightarrow{ }_{21}^{47} \mathrm{Sc}+{ }_{-1}^{0} \mathrm{e}+\mathrm{X}

Identify X .

(electron) anti-neutrino $/ \bar{v}$ ;

[Maximum number: 4]

An experiment is carried out to determine the count rate, corrected for background radiation, when different thicknesses of copper are placed between a radioactive source and a detector. The graph shows the variation of corrected count rate with copper thickness.

Further results were obtained in this experiment with copper and lead absorbers.

Comment on the radiation detected from this radioactive source.

[Maximum number: 2]

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 %.

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

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.

[Maximum number: 1]

An experiment is carried out to determine the count rate, corrected for background radiation, when different thicknesses of copper are placed between a radioactive source and a detector. The graph shows the variation of corrected count rate with copper thickness.

Outline how the count rate was corrected for background radiation.

IB Physics SL E 3 Radioactive Decay Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (c)

Question (d)

Question (i)

Question 2

Question (a)

Question (b)

Question (c)

Question (d)

Question (i)

Question (ii)

Question (iii)

Question 3

Question (a)

Question (b)

Question (c)

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14