Nuclear and Quantum Physics — Free IB Physics SL Practice Questions

1FoundationMCQNuclear fission process1 markPaper 1~2 min

The graph shows binding energy per nucleon as a function of nucleon number

A

. Region Y corresponds to medium-mass nuclei (

A \approx 56

–

90

) and Region Z corresponds to heavy nuclei (

A \approx 200

–

240

). Which statement correctly explains why energy is released when a heavy nucleus in Region Z undergoes fission to produce two nuclei in Region Y?

Solutions

2FoundationMCQNuclear fission process1 markPaper 1~2 min

The binding energy per nucleon of uranium-235 is approximately

7.6 \text{ MeV}

. When uranium-235 undergoes fission, it splits into two fragments with nucleon numbers of approximately 95 and 140, each having a binding energy per nucleon of approximately

8.5 \text{ MeV}

. Which statement correctly explains why energy is released in this process?

Solutions

3FoundationMCQNuclear fission process1 markPaper 1~2 min

The graph shows binding energy per nucleon against nucleon number. Iron-56 has the highest binding energy per nucleon. A uranium-235 nucleus undergoes fission, producing two daughter nuclei with nucleon numbers in the range 90–145. Which statement correctly describes the energy change during this process?

Solutions

4FoundationMCQNuclear fission process1 markPaper 1~2 min

A fission reaction is represented by the equation:

{}^{235}_{92}\text{U} + {}^{1}_{0}\text{n} \rightarrow {}^{141}_{56}\text{Ba} + {}^{92}_{36}\text{Kr} + 3{}^{1}_{0}\text{n}

The binding energy per nucleon of

{}^{235}_{92}\text{U}

is

7.6 \text{ MeV}

and the average binding energy per nucleon of the fission products is

8.4 \text{ MeV}

. What is the approximate energy released in this reaction?

Solutions

5FoundationMCQNuclear fission process1 markPaper 1~2 min

In a nuclear reactor, a moderator slows fast neutrons to thermal speeds. Which statement correctly explains why thermal neutrons are more effective than fast neutrons at inducing fission in uranium-235?

Solutions

6FoundationMCQNuclear fusion and energy production in stars1 markPaper 1~2 min

A binding energy per nucleon graph shows that hydrogen-1 has a binding energy per nucleon of approximately

0\ \text{MeV}

and helium-4 has a binding energy per nucleon of approximately

7.1\ \text{MeV}

. When four hydrogen nuclei fuse to form one helium-4 nucleus, which statement correctly explains why energy is released?

Solutions

7FoundationMCQLife cycle of stars1 markPaper 1~2 min

A star spends several billion years on the main sequence before its luminosity increases by a factor of approximately

10^3

. Which evolutionary stage is responsible for this sharp luminosity increase?

Solutions

8FoundationMCQNuclear fusion and energy production in stars1 markPaper 1~2 min

When two light nuclei undergo fusion in a stellar core, the mass defect is converted to energy according to

E = mc^2

. Which of the following correctly describes the forms in which this energy is released?

Solutions

9FoundationMCQNuclear fusion and energy production in stars1 markPaper 1~2 min

In the core of a main-sequence star, protons undergo repeated fusion reactions. The overall net reaction can be summarised as four protons combining to produce one helium-4 nucleus, releasing energy calculated using

E = mc^2

. The mass of a proton is

1.673 \times 10^{-27}

kg and the mass of a helium-4 nucleus is

6.644 \times 10^{-27}

kg. What is the energy released in this overall reaction?

Solutions

10FoundationMCQNuclear fusion and energy production in stars1 markPaper 1~2 min

In a nuclear fusion reaction in a star, two deuterium nuclei

\left(^2_1\text{H}\right)

fuse to form helium-3

\left(^3_2\text{He}\right)

and a neutron. The total mass of the products is less than the total mass of the reactants. Which statement correctly identifies the source of the energy released?

Solutions

11FoundationMCQIsotopes and atomic mass1 markPaper 1~2 min

A sample of naturally occurring chlorine contains two isotopes: chlorine-35 with an abundance of 75% and chlorine-37 with an abundance of 25%. The isotopic masses are

34.97 \text{ u}

and

36.97 \text{ u}

respectively. What is the relative atomic mass of this chlorine sample?

Solutions

12MasteryMCQIsotopes and atomic mass1 markPaper 1~2 min

Naturally occurring neon contains two stable isotopes:

^{20}

Ne with fractional abundance

0.905

and atomic mass

19.99\text{ u}

, and

^{22}

Ne with fractional abundance

0.095

and atomic mass

21.99\text{ u}

. What is the relative atomic mass of naturally occurring neon?

Solutions

13FoundationMCQAtomic models (Bohr, quantum model)1 markPaper 1~2 min

In the quantum mechanical model of the hydrogen atom, an electron probability cloud is represented as a region of varying dot density around the nucleus. What does a region of higher dot density indicate?

Solutions

14FoundationMCQIsotopes and atomic mass1 markPaper 1~2 min

A mass spectrometer detects three isotopes in a neon sample. The mass of each isotope is taken as equal to its mass number. Isotope — Relative abundance neon-20 — 90.0% neon-21 — 0.3% neon-22 — 9.7% What is the relative atomic mass of this neon sample?

Solutions

15MasteryMCQIsotopes and atomic mass1 markPaper 1~2 min

A uranium ore sample contains two isotopes:

^{235}

U with atomic mass

235.04 \text{ u}

and

^{238}

U with atomic mass

238.05 \text{ u}

. A mass spectrometer determines the relative atomic mass of the sample to be

237.32 \text{ u}

. What is the approximate percentage abundance of

^{235}

U?

Solutions

16FoundationMCQHalf-life and decay constant1 markPaper 1~2 min

The activity of a radioactive sample decreases from 640 Bq to 40 Bq in 20 days. What is the decay constant of this sample?

Solutions

17FoundationMCQRadioactive decay and applications1 markPaper 1~2 min

A radioactive source emits alpha particles, beta particles, and gamma rays, all travelling in the same direction toward the top of the page. A uniform magnetic field is directed into the page. Which type of radiation is deflected toward the left of the page?

Solutions

18FoundationMCQRadioactive decay and applications1 markPaper 1~2 min

A student measures the count rate from a radioactive source at 10-minute intervals. The background count rate is 20 counts per minute. The measured count rates are shown below.

t

/ min — Count rate / counts min

^{-1}

0 — 220 10 — 120 20 — 70 30 — 45 What is the half-life of the source?

Solutions

19FoundationMCQTypes of radiation: Alpha, beta, gamma1 markPaper 1~2 min

An alpha particle is emitted during the radioactive decay of americium-241. Which of the following correctly describes the nature of an alpha particle?

Solutions

20FoundationMCQTypes of radiation: Alpha, beta, gamma1 markPaper 1~2 min

A nucleus undergoes beta-minus decay. Which of the following correctly describes the charge and identity of the emitted beta particle?

Solutions

21FoundationSAQ-SNuclear fission process5 marksPaper 2~8 min

The graph below shows the binding energy per nucleon as a function of mass number

A

.

(a)

Explain why energy is released when a heavy nucleus such as uranium-235 undergoes fission. Refer to the graph in your answer. [2 marks]

(b)

In a fission event, a

^{235}_{92}\text{U}

nucleus splits into two fragments with mass numbers 140 and 95. The binding energy per nucleon read from the graph is

7.6 \ \text{MeV}

for

^{235}\text{U}

,

8.2 \ \text{MeV}

for the fragment with

A = 140

, and

8.5 \ \text{MeV}

for the fragment with

A = 95

. Calculate the energy released in this fission event. [3 marks]

Solutions

22MasterySAQ-SApplications of nuclear fission (nuclear reactors)5 marksPaper 2~8 min

The graph below shows neutron flux (in units of

10^{18}\,\text{m}^{-2}\text{s}^{-1}

) as a function of distance from the centre of a nuclear reactor core.

(a)

Read from the graph the neutron flux at a distance of

2.0\,\text{m}

from the centre. [1 mark]

(b)

A fuel rod is a cylinder of radius

1.0\,\text{cm}

and length

4.0\,\text{m}

. The average neutron flux over the rod is

3.0 \times 10^{18}\,\text{m}^{-2}\text{s}^{-1}

. Calculate the number of neutrons incident one fuel rod per second. [2 marks]

(c)

The non-uniform neutron flux profile means that fuel rods at different radial positions undergo fission at different rates, causing uneven heat generation. Evaluate the design challenge this creates for engineers and suggest how the fuel rod arrangement could address it. [2 marks]

Solutions

23ChallengeSAQ-LNuclear fission process9 marksPaper 2~14 min

Data

- Mass of

{}^{235}_{92}\text{U}

atom

= 235.0439\,\text{u}

- Mass of

{}^{144}_{56}\text{Ba}

atom

= 143.9229\,\text{u}

- Mass of

{}^{90}_{36}\text{Kr}

atom

= 89.9195\,\text{u}

- Mass of neutron

= 1.00867\,\text{u}

-

1\,\text{u} = 931.5\,\text{MeV}\,c^{-2}

The uranium-235 fuel rods in a thermal neutron reactor absorb slow neutrons and undergo fission. One such fission event is represented by:

{}^{235}_{92}\text{U} + {}^{1}_{0}\text{n} \rightarrow {}^{144}_{56}\text{Ba} + {}^{90}_{36}\text{Kr} + 2\,{}^{1}_{0}\text{n}

(a)

Calculate the energy released in this single fission event. Give your answer in MeV. [3 marks]

(b)

The reactor operates at a thermal power of

1.2\,\text{GW}

. Assuming each fission event releases the energy calculated in (a), calculate the mass of

{}^{235}_{92}\text{U}

consumed in

24

hours of continuous operation. Give your answer in grams. [2 marks]

(c)

The neutrons produced in this fission event have kinetic energies of order

1\,\text{MeV}

. Discuss why these neutrons must be slowed to thermal energies (

\sim 0.025\,\text{eV}

) before they can sustain the chain reaction, and explain what determines whether the chain reaction remains self-sustaining rather than dying out or becoming explosive. [4 marks]

Solutions

24FoundationSAQ-LNuclear fission process7 marksPaper 2~11 min

In a nuclear fission experiment, plutonium-239 undergoes fission when struck by a neutron. One possible reaction is:

^{239}_{94}\text{Pu} + \,^{1}_{0}n \rightarrow \,^{145}_{58}\text{Ce} + \,^{92}_{37}\text{Rb} + 3\,^{1}_{0}n

The binding energy per nucleon for

^{239}\text{Pu}

is

7.56 \text{ MeV}

, for

^{145}\text{Ce}

is

8.23 \text{ MeV}

, and for

^{92}\text{Rb}

is

8.69 \text{ MeV}

.

(a)

Determine the total energy released in this fission event. [3 marks]

(b)

Explain why the fission fragments

^{145}\text{Ce}

and

^{92}\text{Rb}

are neutron-rich and state the decay mode by which they move towards stability. [2 marks]

(c)

The complete fission of

1.00 \text{ g}

of

^{239}\text{Pu}

releases energy at a rate of

1.00 \text{ kW}

. Using your answer to (a), determine how many days this fuel supply would last. (

N_A = 6.02 \times 10^{23} \text{ mol}^{-1}

,

1 \text{ MeV} = 1.60 \times 10^{-13} \text{ J}

) [2 marks]

Solutions

25MasterySAQ-SNuclear fission process5 marksPaper 2~8 min

A nuclear waste storage facility monitors the decay of fission products. One significant fission product is strontium-90, which undergoes beta-minus decay. Half-life of strontium-90

= 29\,\text{years}

(a)

State the form in which most of the energy from nuclear fission is initially released. [1 mark]

(b)

The initial activity of a strontium-90 sample is

4.0 \times 10^{12}\,\text{Bq}

. Calculate the time, in years, for the activity to decrease to

5.0 \times 10^{11}\,\text{Bq}

. [2 marks]

(c)

Explain why fission products remain hazardous for many years after the fission event. [2 marks]

Solutions

26FoundationSAQ-SNuclear fusion and energy production in stars7 marksPaper 2~11 min

Consider the fusion of deuterium (

^2_1\text{H}

) and tritium (

^3_1\text{H}

) in a reactor:

^2_1\text{H} + ^3_1\text{H} \rightarrow ^4_2\text{He} + ^1_0\text{n}

The binding energies per nucleus are: deuterium = 2.22 MeV, tritium = 8.48 MeV, helium-4 = 28.3 MeV, neutron = 0 MeV.

(a)

Explain why energy is released in this fusion reaction using the concept of binding energy. [2 marks]

(b)

Calculate the energy released per fusion event, in MeV. [2 marks]

(c)

A reactor undergoes

1.5 \times 10^{20}

fusion events per second. Determine the power output of the reactor in watts. [3 marks]

Solutions

27MasterySAQ-SLife cycle of stars6 marksPaper 2~9 min

A Hertzsprung–Russell (H-R) for a star cluster shows a clear main sequence, a red giant branch, and a horizontal branch. One star, designated Star X, has left the main sequence and is now a red giant.

(a)

State the event that causes a star to leave the main sequence. [1 mark]

(b)

Explain the changes in the core of Star X that cause it to become a red giant. [2 marks]

(c)

The core of Star X contracts while the outer layers expand. The core has mass

M = 2.0 \times 10^{29}\,\text{kg}

and its radius decreases from

R_i = 1.0 \times 10^{8}\,\text{m}

to

R_f = 2.0 \times 10^{7}\,\text{m}

. The gravitational potential energy of a uniform sphere is:

U = -\frac{3GM^2}{5R}

where

G = 6.67 \times 10^{-11}\,\text{N\,m}^2\,\text{kg}^{-2}

. Calculate the change in gravitational potential energy of the core. [3 marks]

Solutions

28ChallengeSAQ-LNuclear fusion and energy production in stars7 marksPaper 2~11 min

Data

-

k = 1.38 \times 10^{-23}\,\text{J\,K}^{-1}

-

1\,\text{eV} = 1.60 \times 10^{-19}\,\text{J}

- Mass of proton

= 1.007276\,\text{u}

- Mass of helium-4 nucleus

= 4.001506\,\text{u}

- Mass of positron

= 0.000548\,\text{u}

-

1\,\text{u} = 931.5\,\text{MeV}\,c^{-2}

- Coulomb barrier for two protons

\approx 0.5\,\text{MeV}

- CNO reaction rate

\propto T^{20}

A star with mass

2.5\,M_\odot

burns hydrogen its core via the CNO cycle, in which carbon-12 acts a catalyst:

^{12}_{6}\text{C} + ^{1}_{1}\text{H} \rightarrow ^{13}_{7}\text{N} + \gamma

^{13}_{7}\text{N} \rightarrow ^{13}_{6}\text{C} + e^{+} + \nu_e

^{13}_{6}\text{C} + ^{1}_{1}\text{H} \rightarrow ^{14}_{7}\text{N} + \gamma

^{14}_{7}\text{N} + ^{1}_{1}\text{H} \rightarrow ^{15}_{8}\text{O} + \gamma

^{15}_{8}\text{O} \rightarrow ^{15}_{7}\text{N} + e^{+} + \nu_e

^{15}_{7}\text{N} + ^{1}_{1}\text{H} \rightarrow ^{12}_{6}\text{C} + ^{4}_{2}\text{He}

The net reaction is:

4\,^{1}_{1}\text{H} \rightarrow ^{4}_{2}\text{He} + 2e^{+} + 2\nu_e + 3\gamma

The star's core temperature is

2.0 \times 10^{7}\,\text{K}

. The average kinetic energy of a proton at this temperature is

E_k = \tfrac{3}{2}kT

.

(a)

Calculate the average kinetic energy of a proton in the star's core in eV. [2 marks]

(b)

Calculate the energy released, in MeV, in the net CNO cycle reaction. [3 marks]

(c)

Explain why fusion can occur even though the average proton kinetic energy found in (a) is far below the Coulomb barrier. [1 mark]

(d)

The core temperature increases to

3.0 \times 10^{7}\,\text{K}

. Determine the factor by which the CNO energy production rate changes. [1 mark]

Solutions

29FoundationSAQ-SNuclear fusion and energy production in stars5 marksPaper 2~8 min

The effective half-life for the first step of proton–proton fusion in the Sun's core is approximately

1.0 \times 10^{10}

years, due to the extremely low probability of the weak-force interaction occurring.

(a)

State why the average kinetic energy of protons in the Sun's core is insufficient to overcome the Coulomb barrier classically. [1 mark]

(b)

Explain how proton–proton fusion nevertheless proceeds, and why the reaction rate remains extremely slow. [2 marks]

(c)

A region of the Sun's core initially contains

1.0 \times 10^{50}

protons. Calculate the number of protons remaining after

2.0 \times 10^{10}

years, using

N = N_0 \left(\dfrac{1}{2}\right)^{t/t_{1/2}}

. [2 marks]

Solutions

30MasterySAQ-SLife cycle of stars8 marksPaper 2~12 min

Data

- Initial density of cloud:

\rho_0 = 1.6 \times 10^{-19}\,\text{kg m}^{-3}

- Initial radius of cloud:

R_0 = 3.0 \times 10^{15}\,\text{m}

- Gravitational constant:

G = 6.67 \times 10^{-11}\,\text{N m}^2\,\text{kg}^{-2}

A protostar forms from a collapsing molecular cloud of hydrogen gas. As it collapses under gravity, gravitational potential energy is converted into thermal energy, raising the core temperature.

(a)

State the energy conversion that occurs during the gravitational collapse of the molecular cloud. [1 mark]

(b)

Show that the mass of the protostar is approximately

2.0 \times 10^{30}\,\text{kg}

. [2 marks]

(c)

The protostar contracts to a final radius of

7.0 \times 10^8\,\text{m}

. Calculate the average density of the protostar at this radius. [2 marks]

(d)

The minimum temperature required for hydrogen fusion is approximately

10^7\,\text{K}

. The mean thermal energy per particle is

E_\text{th} \approx \frac{3}{2}k_BT

, where

k_B = 1.38 \times 10^{-23}\,\text{J K}^{-1}

. The Coulomb barrier energy between two protons separated by

d = 1.0 \times 10^{-15}\,\text{m}

is given by

E_C = \frac{e^2}{4\pi\varepsilon_0 d}

, where

\frac{e^2}{4\pi\varepsilon_0} = 1.44 \times 10^{-9}\,\text{eV m}

. Determine the ratio

\dfrac{E_C}{E_\text{th}}

at

T = 10^7\,\text{K}

, and hence explain why quantum tunnelling is necessary for fusion to occur at this temperature. [3 marks]

Solutions

31MasterySAQ-SAtomic models (Bohr, quantum model)5 marksPaper 2~8 min

Data

1\,\text{eV} = 1.60 \times 10^{-19}\,\text{J}

,

c = 3.00 \times 10^{8}\,\text{m\,s}^{-1}

,

h = 6.63 \times 10^{-34}\,\text{J\,s}

,

E_n = -\dfrac{13.6}{n^2}\,\text{eV}

A medical physicist studies the emission spectrum of hydrogen gas. She observes a photon of wavelength

486\,\text{nm}

emitted when an electron in a hydrogen atom transitions from a higher energy level to the

n = 2

level. The energy of the

n = 2

level is

-3.40\,\text{eV}

.

(a)

State one feature of the Bohr model that explains why hydrogen emits only discrete wavelengths of light. [1 mark]

(b)

Calculate the energy of the

486\,\text{nm}

photon in eV. [2 marks]

(c)

Show that the initial energy level of the electron is

n = 4

. [2 marks]

Solutions

32MasterySAQ-SAtomic models (Bohr, quantum model)5 marksPaper 2~8 min

Data

1\,\text{eV} = 1.60 \times 10^{-19}\,\text{J}

;

h = 6.63 \times 10^{-34}\,\text{J\,s}

;

c = 3.00 \times 10^{8}\,\text{m\,s}^{-1}

Relevant equations:

E = hf

,

\;c = f\lambda

A research team at a nuclear facility is analysing the emission spectrum of helium ions (

\text{He}^+

). These ions have a single electron orbiting a nucleus of charge

+2e

. The energy levels are given by

E_n = -\dfrac{54.4}{n^2}\,\text{eV}

. A transition from

n = 4

to

n = 2

is observed.

(a)

State one difference between the Bohr model and the quantum mechanical model regarding the location of an electron. [1 mark]

(b)

Calculate the energy, in joules, of the photon emitted during the transition from

n = 4

to

n = 2

. [2 marks]

(c)

Deduce whether the emitted photon lies in the ultraviolet, visible, or infrared region of the electromagnetic spectrum. [2 marks]

Solutions

33ChallengeSAQ-LAtomic models (Bohr, quantum model)7 marksPaper 2~11 min

Data

- Rydberg constant:

R_H = 1.097 \times 10^7\,\text{m}^{-1}

- Planck constant:

h = 6.63 \times 10^{-34}\,\text{J\,s}

- Speed of light:

c = 3.00 \times 10^8\,\text{m\,s}^{-1}

- Ground state energy of hydrogen:

E_1 = -13.6\,\text{eV}

-

1\,\text{eV} = 1.60 \times 10^{-19}\,\text{J}

Formulae:

\dfrac{1}{\lambda} = R_H\!\left(\dfrac{1}{n_f^2} - \dfrac{1}{n_i^2}\right)

;

\quad E_n = \dfrac{E_1}{n^2}

;

\quad E = hf = \dfrac{hc}{\lambda}

The hydrogen spectrum in the visible region includes the Balmer series, where electrons transition to the

n = 2

energy level. A spectral line is observed at a wavelength of

486\,\text{nm}

.

(a)

Calculate the initial energy level

n_i

from which the electron transitioned to produce the

486\,\text{nm}

spectral line. [3 marks]

(b)

Show that the energy of the photon emitted at

486\,\text{nm}

is consistent with the energy difference

\Delta E = E_{n_i} - E_2

predicted by the Bohr model. [2 marks]

(c)

Evaluate one limitation of the Bohr model that is revealed by examining the fine structure of hydrogen spectral lines, and state how the quantum mechanical model addresses it. [2 marks]

Solutions

34MasterySAQ-SAtomic models (Bohr, quantum model)5 marksPaper 2~8 min

Data

h = 6.63 \times 10^{-34}\,\text{J\,s}

,

c = 3.00 \times 10^{8}\,\text{m\,s}^{-1}

,

1\,\text{eV} = 1.60 \times 10^{-19}\,\text{J}

E_n = -\frac{13.6}{n^2}\,\text{eV} \qquad E = hf \qquad c = f\lambda

A student uses a gas discharge tube filled with hydrogen. Four visible spectral lines are observed: red (

656\,\text{nm}

), blue-green (

486\,\text{nm}

), violet (

434\,\text{nm}

), and deep violet (

410\,\text{nm}

). These lines form the Balmer series, with all transitions ending at

n = 2

.

(a)

State what is meant by a spectral series in the Bohr model of hydrogen. [1 mark]

(b)

Calculate the energy difference, in eV, between the

n = 3

and

n = 2

levels. [2 marks]

(c)

The red line at

656\,\text{nm}

is the longest-wavelength line in the Balmer series. Explain, without further calculation, why this line must correspond to the transition from the lowest available upper level to

n = 2

. [2 marks]

Solutions

35MasterySAQ-SAtomic models (Bohr, quantum model)5 marksPaper 2~8 min

Data

h = 6.63 \times 10^{-34}\,\text{J\,s}

,

c = 3.00 \times 10^{8}\,\text{m\,s}^{-1}

,

1\,\text{eV} = 1.60 \times 10^{-19}\,\text{J}

Relevant equations:

E = hf

,

c = f\lambda

,

E_n = -\dfrac{13.6}{n^2}\,\text{eV}

A technician calibrates a spectrometer using a hydrogen discharge lamp. The lamp produces a spectral line at wavelength

434\,\text{nm}

, corresponding to a transition that ends at

n = 2

.

(a)

State the condition required for an electron in the Bohr model to emit a photon. [1 mark]

(b)

Calculate the energy, in joules, of a photon of wavelength

434\,\text{nm}

. [2 marks]

(c)

Determine the initial energy level

n_i

of the electron responsible for this spectral line, and justify your answer. [2 marks]

Solutions

36ChallengeSAQ-LRadioactive decay and applications9 marksPaper 2~14 min

Data

- Initial activity of the sample:

A_0 = 800\,\text{MBq}

- Atomic mass of fluorine-18:

m(\text{F-18}) = 2.98850 \times 10^{-26}\,\text{kg}

- Atomic mass of oxygen-18:

m(\text{O-18}) = 2.98762 \times 10^{-26}\,\text{kg}

- Mass of a positron:

m_{e^+} = 9.11 \times 10^{-31}\,\text{kg}

- Speed of light:

c = 3.00 \times 10^{8}\,\text{m\,s}^{-1}

A medical cyclotron produces a pure sample of the radioisotope fluorine-18 (

^{18}_{9}\text{F}

) for use in PET scans. Fluorine-18 decays via positron emission to oxygen-18 (

^{18}_{8}\text{O}

) with a half-life of 110 minutes.

(a)

(i) Calculate the decay constant of fluorine-18. [1]
(ii) Determine the number of fluorine-18 atoms in the sample at the instant is produced. [2 marks]

(b)

(i) Explain why the energy released per decay cannot be calculated from the difference in atomic masses of fluorine-18 and oxygen-18 alone. [2]
(ii) Calculate the energy, in MeV, released in a single fluorine-18 decay. [2 marks]

(c)

Determine the time, in hours, after production at which the activity of the sample falls to

25\,\text{MBq}

. [2 marks]

Solutions

37MasterySAQ-SHalf-life and decay constant5 marksPaper 2~8 min

Data

1\,\text{year} = 3.16 \times 10^{7}\,\text{s}

A sample of cobalt-60, used in radiotherapy machines, has a decay constant of

\lambda = 4.2 \times 10^{-9}\,\text{s}^{-1}

. The graph shows the activity of the sample over time. The curve starts at

A_0 = 8.0 \times 10^{14}\,\text{Bq}

; at

t = 5.3\,\text{years}

the activity is

4.0 \times 10^{14}\,\text{Bq}

; at

t = 10.6\,\text{years}

the activity is

2.0 \times 10^{14}\,\text{Bq}

.

(a)

Calculate the half-life of cobalt-60 in years using the decay constant. [2 marks]

(b)

Determine the initial number of cobalt-60 nuclei in the sample. [2 marks]

(c)

A medical physicist states that after three half-lives the sample is no longer suitable for radiotherapy because its activity has fallen below

1.0 \times 10^{14}\,\text{Bq}

. Evaluate this statement. [1 mark]

Solutions

38ChallengeSAQ-LRadioactive decay and applications7 marksPaper 2~11 min

Data

A_0 = 200\,\text{kBq}, \quad T_{1/2} = 5.27\,\text{years}, \quad 1\,\text{year} = 3.15 \times 10^7\,\text{s}

A cobalt-60 source (

^{60}_{27}\text{Co}

) is used industrial radiography to detect flaws in metal welds. Cobalt-60 decays by beta-minus emission to nickel-60 (

^{60}_{28}\text{Ni}

) with a half-life of

5.27

years. A technician uses a source with an initial activity of

200\,\text{kBq}

.

(a)

(i) Calculate the decay constant of cobalt-60 in

\text{s}^{-1}

. [1]
(ii) Using your answer to (a)(i), determine the initial number of cobalt-60 atoms in the source. [2 marks]

(b)

Cobalt-60 has 27 protons and 33 neutrons. Deduce, with reference to the nuclear composition of cobalt-60, why beta-minus decay must involve the transformation of a neutron rather than a proton. [2 marks]

(c)

Determine the time, in years, after which the activity of the source drops to

12.5\,\text{kBq}

. [2 marks]

Solutions

39ChallengeSAQ-LRadioactive decay and applications7 marksPaper 2~11 min

A nuclear reactor produces technetium-99m (

^{99\text{m}}_{43}\text{Tc}

), a metastable isomer used in medical imaging. It decays via gamma emission to technetium-99 (

^{99}_{43}\text{Tc}

) with a half-life of

6.01

hours. The gamma photon emitted has an energy of

140\,\text{keV}

(

= 2.24 \times 10^{-14}\,\text{J}

). A hospital receives a sample with an initial activity of

500\,\text{MBq}

.

h = 6.63 \times 10^{-34}\,\text{J\,s} \qquad 1\,\text{hour} = 3600\,\text{s}

(a)

Calculate the decay constant of technetium-99m. [2 marks]

(b)

Explain why gamma decay does not change the atomic number or mass number of the nucleus. [2 marks]

(c)

Determine the total energy, in joules, released by the sample in the first

12.0

hours after receipt. [3 marks]

Solutions

40ChallengeSAQ-LRadioactive decay and applications8 marksPaper 2~12 min

A medical physics laboratory uses a sample of technetium-99m (

^{99m}_{43}\text{Tc}

) for diagnostic imaging. Technetium-99m is a metastable isotope that decays by gamma emission to technetium-99 (

^{99}_{43}\text{Tc}

).

T_{1/2} = 6.0\,\text{hours} \qquad A_0 = 2.4 \times 10^8\,\text{Bq} \qquad 1\,\text{hour} = 3600\,\text{s}

(a)

Calculate the decay constant

\lambda

of technetium-99m, giving your answer in

\text{s}^{-1}

. [2 marks]

(b)

Determine the number of technetium-99m nuclei present in the sample at

t = 0

. [2 marks]

(c)

Evaluate why technetium-99m is a more suitable radioisotope for diagnostic imaging than a pure beta-emitting isotope of similar half-life. In your answer, refer to the nature of the emitted radiation, its interaction with body tissue, and the suitability of the half-life for a clinical procedure lasting approximately 4–6 hours. [4 marks]

Solutions

Nuclear and Quantum Physics — Free Physics SL Practice Questions