Question 1a

Marks: 5

In a scattering experiment, a metal foil of thickness 0.4 µm scatters 1 in 20 000 alpha particles through an angle greater than 90°.

(a)

(i)

Considering the metal foil as a number of layers of atoms, n, explain why the probability of an alpha particle being deflected by a given atom is approximately equal to

\frac{1}{20 000 n}

[2]

(ii)

Estimate the diameter of the nucleus. Consider the nuclei as cubes and the atoms in the foil as cubes of side length 0.25 nm.

[3]

Question 1b

Marks: 3

Deviations from Rutherford scattering are observed when high-energy alpha particles are incident on nuclei.

(b)

Outline the incorrect assumption used in the Rutherford scattering formula and suggest an explanation for the observed deviations.

[3]

Question 1c

Marks: 3

In a scattering experiment, alpha particles were directed at five different thin metallic foils, as shown in the table.

Metal	Symbol
Silver	${}_{47}^{108}{Ag}$
Aluminium	${}_{13}^{27}{Al}$
Gold	${}_{79}^{197}{Au}$
Tin	${}_{50}^{119}{Sn}$
Tungsten	${}_{74}^{184}W$

Initially, all alpha particles have the same energy. This energy is gradually increased.

(c)

Predict and explain the differences in deviations from Rutherford scattering that will be observed.

[3]

Question 1d

Marks: 3

(d)

Outline why the particles must be accelerated to high energies in scattering experiments.

[3]

Question 2a

Marks: 3

(a)

Show that the decay constant is related to the half-life by the expression

$λ T_{\frac{1}{2}} = \ln 2$

[3]

Question 2b

Marks: 3

Uranium-238 has a half-life of 4.47 × 10⁹ years and decays to thorium-234. The thorium decays (by a series of further nuclear processes with short half-lives) to lead.

(b)

Assuming that a rock was originally entirely uranium and that at present, 1.5% of the nuclei are now lead, calculate the age of the rock. Give your answer in years to 2 significant figures.

[3]

Question 2c

Marks: 3

The ionisation current I produced by α-particles emitted in the decay of radon can be measured experimentally. The logarithmic graph shows how current, ln I, varies with time, t.

9Ny8MkHj_12-2-ib-hl-sqs-hard-q5b-question

(c)

Using the graph, determine the half-life of radon.

[3]

Question 3a

Marks: 3

An electron beam of energy 1.3 × 10⁻¹⁰ J is used to study the nuclear radius of beryllium-9. The beam is directed from the left at a thin sample of beryllium-9. A detector is placed at an angle θ relative to the direction of the incident beam.

12-1-ib-hl-sqs-easy-q1b-question

The radius of a beryllium-9 nucleus is 2.9 × 10⁻¹⁵ m. The beryllium-9 nuclei behave like a diffraction grating.

(a)

Sketch the expected variation of electron intensity against the angle from the horizontal.

[3]

Question 3b

Marks: 3

The isotope beryllium-10 is formed when a nucleus of deuterium $({}_{1}^{2}H)$ collides with a nucleus of beryllium-9 $({}_{4}^{9}{Be})$ . The radius of a deuterium nucleus is 1.5 fm.

(b)

(i)

Determine the minimum initial kinetic energy, in J, that the deuterium nucleus must have in order to produce the isotope beryllium-10.

[2]

(ii)

Outline an assumption made in this calculation.

[1]

Question 3c

Marks: 4

The nucleus of beryllium-9 is replaced by a nucleus of gold-197.

(c)

Suggest the change, if any, to the following:

(i)

Distance of closest approach of a deuterium nucleus.

[2]

(ii)

Angle of minimum intensity from electron scattering. Assume the electrons have the same energy as in part (a).

[2]

Question 4a

Marks: 2

Unstable uranium-238 has various nuclear decay modes to become stable thorium-234. The total amount of energy released when it decays is measured to be 210 keV.

q1b

(a)

Outline, without calculation, the intermediate decay modes between the unstable uranium-238 to the stable thorium-234.

[2]

Question 4b

Marks: 4

A possible decay chain for uranium-238 is:

${}_{92}^{238}U \to {}_{90}^{234}{T h^{*}} + {}_{2}^{4}α$

${}_{90}^{234}{T h^{*}} \to {}_{90}^{234}{T h^{*}} + γ$

${}_{90}^{234}{T h^{*}} \to {}_{90}^{234}{T h} + γ$

(b)

Calculate the total amount of energy, in joules, carried away as gamma radiation in this decay chain.

[4]

Question 4c

Marks: 2

(c)

Deduce an alternative decay chain from unstable uranium-238 to stable thorium-234 which releases the same amount of energy in the form of gamma radiation as in part (b).

Justify your answer with a calculation.

[2]

Question 5a

Marks: 3

The half-life of uranium-238 is so long in comparison to any of the isotopes in its decay chain that we can assume the number of lead-206 nuclei, $N_{P b}$ at any time is equal to the number of uranium-238 that have decayed.

The number of uranium-238 nuclei $N_{U}$ at time t is given by the equation:

$N_{U} = N_{0} e^{- λ t}$

Where $N_{0}$ is the number of uranium-238 nuclei at t = 0.

(a)

Show that the ratio of

N_{P b}

to

N_{U}

is given by:

\frac{N_{P b}}{N_{U}} = e^{λ t} - 1

[3]

Question 5b

Marks: 3

Enriched uranium fuel is a mixture of the fissionable uranium-235 with the more naturally abundant uranium-238. Mixtures of radioactive nuclides such as this are very common in the nuclear power industry.

Two samples of radioactive nuclides X and Y each have an activity of A₀ at t = 0. They are subsequently mixed together.

The half-lives of X and Y are 16 and 8 years respectively.

(b)

Show that the total activity of the mixture at time t = 48 years is equal to:

\frac{9}{64} A_{0}

[3]

DP IB Physics: HL

Topic Questions

12.2 Nuclear Physics

Question 1a

Question 1b

Question 1c

Question 1d

Question 2a

Question 2b

Question 2c

Question 3a

Question 3b

Question 3c

Question 4a

Question 4b

Question 4c

Question 5a

Question 5b

Resources

Members

Company

Quick Links