DP Physics (last assessment 2024)

Question 20N.2.HL.TZ0.10c

Date	November 2020	Marks available	[Maximum mark: 2]	Reference code	20N.2.HL.TZ0.10c
Level	HL	Paper	2	Time zone	TZ0
Command term	Show that	Question number	c	Adapted from	N/A

[Maximum mark: 2]

20N.2.HL.TZ0.10c

The de Broglie wavelength $λ$ of a particle accelerated close to the speed of light is approximately

$λ \approx \frac{h c}{E}$

where $E$ is the energy of the particle.
A beam of electrons of energy $4.2 \times 10^{8} eV$ is produced in an accelerator.

(c)

Experiments with many nuclides suggest that the radius of a nucleus is proportional to $A^{\frac{1}{3}}$ , where $A$ is the number of nucleons in the nucleus. Show that the density of a nucleus remains approximately the same for all nuclei.

[2]

Markscheme

volume of a nucleus proportional to ${(A^{\frac{1}{3}})}^{3} = A$ AND mass proportional to $A$ ✓

the ratio $\frac{mass}{volume}$ independent of $A$ «hence density the same for all nuclei» ✓

Both needed for MP1

Examiners report

This question proved challenging and it wasn't common to find answers that scored both marks. Of those that had the right approach some missed out on both marks by describing A as the mass of the nucleus rather than proportional to the mass of the nucleus.

Syllabus sections

Additional higher level (AHL)

Additional higher level (AHL) » Topic 12: Quantum and nuclear physics » 12.2 – Nuclear physics

Additional higher level (AHL) » Topic 12: Quantum and nuclear physics

Question 20N.2.HL.TZ0.10c

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