IB Physics SL E Nuclear & Quantum

[Maximum number: 11]

This question is in two parts. Part 1 is about the nuclear model of the atom and radioactive decay. Part 2 is about waves.

Part 1 Nuclear model of the atom and radioactive decay

(a)

Outline how the evidence supplied by the Geiger-Marsden experiment supports the nuclear model of the atom.

[ 4 ]

(b)

The nuclide radium-226 $\left({ }_{88}^{226} \mathrm{Ra}\right)$ decays into an isotope of radon (Rn) by the emission of an alpha particle and a gamma-ray photon.

[ 7 ]

(i)

State what is meant by the terms nuclide and isotope.

Nuclide:
Isotope:

[ 2 ]

(ii)

Construct the nuclear equation for the decay of radium-226.

{ }_{88}^{226} \mathrm{Ra} \rightarrow{ }_{\ldots \ldots \ldots \ldots . .}^{\ldots \ldots \ldots . .} \mathrm{Rn}+{ }_{\ldots \ldots \ldots . .}^{\ldots \ldots \ldots . .} \mathrm{He}+{ }_{\ldots \ldots \ldots . .}^{\ldots \ldots \ldots . .} \gamma

[ 3 ]

${ }_{86}^{222} \mathrm{Rn}$ ;
${ }_{2}^{4} \mathrm{He}$ or ${ }_{0}^{0} \gamma$ ;
top and bottom numbers balanced correctly;

(iii)

Radium-226 has a half-life of 1600 years. Determine the time, in years, it takes for the activity of radium-226 to fall to $\frac{1}{64}$ of its original activity.
Part 2 Waves
Two waves, A and B, are travelling in opposite directions in a tank of water. The graph shows the variation of displacement of the water surface with distance along the wave at a particular instant.

Figure for Question (iii) — IB Physics SL

[ 2 ]

[Maximum number: 9]

(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} .

[ 3 ]

(i)

Identify the proton number Z of X.

Z=

[ 1 ]

(ii)

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: 6]

This question is in two parts. Part 1 is about energy resources. Part 2 is about thermal physics.
Part 1 Energy resources
Electricity can be generated using nuclear fission, by burning fossil fuels or using pump storage hydroelectric schemes.

(a)

In a nuclear reactor, outline the purpose of the

[ 3 ]

(i)

heat exchanger.

[ 1 ]

(ii)

moderator.

[ 2 ]

(b)

Fission of one uranium-235 nucleus releases 203 MeV .

[ 3 ]

(i)

Determine the maximum amount of energy, in joule, released by 1.0 g of uranium-235 as a result of fission.

[ 3 ]

( 203 MeV is equivalent to) $3.25 \times 10^{-11} \mathrm{~J}$ ;
$6.02 \times 10^{23}$ nuclei have a mass of $235 \mathrm{~g} /$ evaluates number of nuclei;
( $2.56 \times 10^{21}$ nuclei produce) $8.32 \times 10^{10} \mathrm{~J} /$ multiplies two previous answers;

[Maximum number: 10]

The diagram shows a simplified energy-balance model for the Earth surface–atmosphere system.

Figure for Question E. Nuclear and quantum physics question 4 — IB Physics SL

The following data are given:

\begin{aligned} \text { Average albedo of Earth } & =0.30 \\ \text { Average global temperature of the surface } & =288 \mathrm{~K} \\ \text { Average Earth-Sun distance } & =1.5 \times 10^{11} \mathrm{~m} \end{aligned}

(a)

The primary energy source of the Sun is the proton-proton (p-p) chain of fusion reactions. Four protons and two electrons produce a helium nucleus together with neutrinos and gamma photons. The overall reaction is:

4{ }_{1}^{1} \mathrm{p}+2{ }_{-1}^{0} \mathrm{e} \rightarrow{ }_{2}^{4} \mathrm{He}+2{ }_{0}^{0} v_{e}+4 \gamma

[ 6 ]

(i)

The mass of the helium nucleus is 4.001506 u . Calculate, in MeV , the energy released in the reaction.

[ 2 ]

ALTERNATIVE 1
$\begin{aligned} & \Delta m=4 \times 1.007276+2 \times 0.000549-4.001506 «=0.028696 \mathrm{u} » \vee & \text { « } 0.028696 \times 931.5=\text { » } 26.7 \mathrm{MeV} \end{aligned}$

ALTERNATIVE 2
$\begin{aligned} & \Delta m=4 \times 938+2 \times 0.511-4.001506 \times 931.5 \ll=25.6 \mathrm{MeV} \mathrm{c}^{-2} \gg & 25.6 \mathrm{MeV} \end{aligned}$

Marks can only be awarded from one Alternative

Unit is not required.

Particle masses in u and $M e V c^{-2}$ lead to differently rounded answers, working must be checked.

Award [1] max if electrons are omitted. This leads to ALT $125.7 \ll \mathrm{MeV} \gg$ , ALT $224.6 \ll \mathrm{MeV} \gg$

Award ECF if incorrect number of particles used e.g. 1 electron rather than 2.

(ii)

Outline the role of fusion reactions in maintaining a stable radius of the Sun.

[ 2 ]

(iii)

Outline how the presence of helium in the Sun can be confirmed empirically.

[ 2 ]

(b)

The positions of the Sun and the star Antares are shown in the Hertzsprung-Russell (HR) diagram.

[ 4 ]

(i)

State the star type of Antares.

[ 1 ]

(ii)

Discuss how nuclear fusion processes in Antares are different from those in the Sun.

[ 3 ]

IB Physics SL E: Nuclear and Quantum Physics

Covered syllabus points

Covered syllabus points

E. Nuclear and quantum physics question 1

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

E. Nuclear and quantum physics question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

Question (c)

Question (d)

Question (i)

E. Nuclear and quantum physics question 3

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

E. Nuclear and quantum physics question 4

Question (a)

Question (i)

Question (ii)

Question (iii)

Question (b)

Question (i)

Question (ii)