DP Physics (last assessment 2024)

Question 23M.3.HL.TZ1.18

Date	May 2023	Marks available	[Maximum mark: 5]	Reference code	23M.3.HL.TZ1.18
Level	HL	Paper	3	Time zone	TZ1
Command term	Calculate, Demonstrate, Show that	Question number	18	Adapted from	N/A

18.

[Maximum mark: 5]

23M.3.HL.TZ1.18

(a)

Light from a distant intergalactic cloud shows a redshift of 1.74. Show that the size of the universe when the light was emitted, relative to its present size, is 0.365.

[1]

Markscheme

« $z = \frac{R}{R_{0}} - 1 \Rightarrow$ » $\frac{R_{0}}{R} = \frac{1}{1 + z} = \frac{1}{2.74}$ = 0.36496 ✓

Examiners report

Cosmic scale factor. The cosmic scale factor is a well-known concept by the students, as seen in answers to a), but applications and use of proportionality in this context showed strong discrimination between average and better students.

(b.i)

Demonstrate that the temperature of the cosmic microwave background (CMB) radiation is proportional to $\frac{1}{R}$
where R is the cosmic scale factor of the universe.

[2]

Markscheme

«physical lengths are proportional to R so $\frac{λ}{R} = \frac{λ_{0}}{R_{0}}$ » ✓

use of Wien’s law $λ$ T = const to get result✓

(b.ii)

The temperature of the CMB has been measured by studying carbon absorption lines in the intergalactic cloud in (a). The temperature measured is 7.4 K.

Calculate the present value of the CMB temperature.

[2]

Markscheme

T = T₀ $\frac{R_{0}}{R}$ OR $\frac{T}{T_{0}} = \frac{R_{0}}{R}$ OR TR = T₀R₀ ✓

T = 7.4 × 0.365 = 2.7 «K» ✓

Question 23M.3.HL.TZ1.18

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