DP Physics (last assessment 2024)

Question 18N.2.HL.TZ0.6

Date	November 2018	Marks available	[Maximum mark: 12]	Reference code	18N.2.HL.TZ0.6
Level	HL	Paper	2	Time zone	TZ0
Command term	Calculate, Determine, Explain, Show that, State	Question number	6	Adapted from	N/A

[Maximum mark: 12]

18N.2.HL.TZ0.6

(a.i)

State how the density of a nucleus varies with the number of nucleons in the nucleus.

[1]

Markscheme

it is constant ✔

(a.ii)

Show that the nuclear radius of phosphorus-31 ( ${}_{15}^{31}{\text{P}}$ ) is about 4 fm.

[1]

Markscheme

R = ${\text{1}}{\text{.20}} \times {10^{ - 15}} \times {31^{\frac{1}{3}}} = 3.8 \times {10^{ - 15}}$ «m» ✔

Must see working and answer to at least 2SF

${}_{15}^{32}{\text{P}}$ is formed when a nucleus of deuterium ( ${}_{1}^{2}{\text{H}}$ ) collides with a nucleus of ${}_{15}^{31}{\text{P}}$ . The radius of a deuterium nucleus is 1.5 fm.

(b.i)

State the maximum distance between the centres of the nuclei for which the production of ${}_{15}^{32}{\text{P}}$ is likely to occur.

[1]

Markscheme

separation for interaction = 5.3 or 5.5 «fm» ✔

(b.ii)

Determine, in J, the minimum initial kinetic energy that the deuterium nucleus must have in order to produce ${}_{15}^{32}{\text{P}}$ . Assume that the phosphorus nucleus is stationary throughout the interaction and that only electrostatic forces act.

[2]

Markscheme

energy required = $\frac{{15{e^2}}}{{4\pi {\varepsilon _0} \times 5.3 \times {{10}^{ - 15}}}}$ ✔

= 6.5 / 6.6 ×10⁻¹³ OR 6.3 ×10⁻¹³«J» ✔

Allow ecf from (b)(i)

(c)

${}_{15}^{32}{\text{P}}$ undergoes beta-minus (β^–) decay. Explain why the energy gained by the emitted beta particles in this decay is not the same for every beta particle.

[2]

Markscheme

«electron» antineutrino also emitted ✔

energy split between electron and «anti»neutrino ✔

(d.i)

State what is meant by decay constant.

[2]

Markscheme

probability of decay of a nucleus ✔

the fraction of the number of nuclei that decay

in one/the next second

per unit time ✔

(d.ii)

In a fresh pure sample of ${}_{15}^{32}{\text{P}}$ the activity of the sample is 24 Bq. After one week the activity has become 17 Bq. Calculate, in s^–1, the decay constant of ${}_{15}^{32}{\text{P}}$ .