CAIE A-Level Physics A2 23 Nuclear Physics Questions

Practise using mass defect, binding energy, nuclear equations and decay laws to calculate energy release, compare reactions and interpret radioactive data.

Exam points

use mass-energy equivalence, nuclear equations and mass defect to analyse nuclear reactions
interpret binding-energy-per-nucleon data to explain and compare fusion, fission and energy release
calculate nuclear energy release from mass change or binding-energy change
explain the random and spontaneous nature of radioactive decay using count-rate evidence
calculate activity and decay constant from A = ?N and half-life relationships
model and interpret exponential radioactive decay using equations, graphs and measured data

Covered syllabus points

23.1 Mass defect and nuclear binding energy 23.2 Radioactive decay

[Maximum number: 1]

Use data from (b) to calculate the mass that is converted into energy every second in the Sun.
mass = kg

$\begin{aligned} m=\frac{E}{c^{2}} =\frac{3.83 \times 10^{26}}{3.00 \times 10^{82}} =4.26 \times 10^{9} \mathrm{~kg} \end{aligned}$

[Maximum number: 6]

Carbon-15 $\left({ }_{6}^{15} \mathrm{C}\right)$ is an isotope of carbon that undergoes radioactive decay to nitrogen-15 $\left({ }_{7}^{15} \mathrm{~N}\right)$ , which is a stable isotope of nitrogen.

Radioactive decay is both a random and a spontaneous process.

(a)

State what is meant by:

[ 2 ]

(i)

random

[ 1 ]

(ii)

spontaneous.

[ 1 ]

(b)

A small sample of carbon-15 decays. The mass M of carbon-15 in the sample decreases with time t.

Fig. 10.1 shows the variation with t of the value of $\ln \left(M / 10^{-16} \mathrm{~g}\right)$ .

Fig. 10.1

[ 2 ]

(i)

State how Fig. 10.1 demonstrates that radioactive decay is random.

[ 1 ]

(ii)

Use your answer in (b)(iv) to calculate the half-life of carbon-15.
half-life = s

[ 1 ]

half-life $=0.693 / \lambda$ $\text { = } 0.693 \text { / } 0.28$ $=2.5 \mathrm{~s}$

(c)

The equation for the decay of carbon- 15 can be written as

{ }_{6}^{15} \mathrm{C} \rightarrow{ }_{7}^{15} \mathrm{~N}+{ }_{-1}^{0} \beta+{ }_{0}^{0} \bar{v} .

State and explain how the mass of the products of the decay must compare with the mass of the carbon-15 nucleus.

[ 2 ]

[Maximum number: 10]

One nuclear reaction that can take place in a nuclear reactor may be represented, in part, by the equation

{ }_{92}^{235} \mathrm{U}+{ }_{0}^{1} \mathrm{n} \rightarrow{ }_{42}^{95} \mathrm{Mo}+{ }_{57}^{139} \mathrm{La}+2{ }_{0}^{1} \mathrm{n}+\ldots \ldots \ldots \ldots .+ \text { energy }

Data for a nucleus and some particles are given in Fig. 12.1.

Fig. 12.1

(a)

Complete the nuclear reaction shown above.

[ 1 ]

$7{ }_{-1}^{0} \mathrm{e}$

(b)

Show that the energy equivalent to 1.00 u is 934 MeV .

[ 3 ]

$E=m c^{2}$ $=1.66 \times 10^{-27} \times\left(3.00 \times 10^{8}\right)^{2}$ $=1.494 \times 10^{-10} \mathrm{~J}$

division by $1.60 \times 10^{-13}$ clear to give 934 MeV

(c)

Calculate the binding energy per nucleon, in MeV , of lanthanum-139 $\left({ }_{57}^{139} \mathrm{La}\right)$ . MeV

[ 3 ]

$\begin{aligned} \Delta m =(82 \times 1.00863 u)+(57 \times 1.00728 u)-138.955 u =(-) 1.16762(u) \end{aligned}$
energy $=1.16762 \times 934$
energy per nucleon $=(1.16762 \times 934) / 139$ $=7.85 \mathrm{MeV}$

(d)

State and explain whether the binding energy per nucleon of uranium-235 $\left({ }_{92}^{235} \mathrm{U}\right)$ will be greater, equal to or less than your answer in (b)(ii).

[ 3 ]

[Maximum number: 9]

Carbon-11 is radioactive and decays by $\beta^{+}$ emission to form boron-11. Carbon-11 has a half-life of 20 minutes. Boron-11 is stable.

(a)

Define half-life.

[ 1 ]

(b)

A sample contains $N_{0}$ nuclei of carbon-11 and no other nuclei at time t=0.

On Fig. 9.1, sketch the variation with t of the number of nuclei of boron-11 in the sample.

Fig. 9.1

[ 3 ]

sketch: line with positive gradient starting at (0,0) and extending to $t=80 \mathrm{~min}$
exponential curve, extending from t=0 to $t=80 \mathrm{~min}$ , with gradient of steadily decreasing magnitude
line passing through $(0,0),\left(20,0.5 N_{0}\right)$ and $\left(40,0.75 N_{0}\right)$

(c)

Explain, with reference to the random nature of radioactive decay, why the activity of the carbon-11 sample in (b) decreases with time.

[ 2 ]

(d)

State, with reasons, whether a radiation detector placed near to the sample of carbon-11 indicates a measured count rate from the sample that is less than, the same as or greater than the activity of the sample.

[ 3 ]

All question bank results loaded

Covered syllabus points

Question 1

Question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

Question (c)

Question 3

Question (a)

Question (b)

Question (c)

Question (d)

Question 4

Question (a)

Question (b)

Question (c)

Question (d)