DP Physics (last assessment 2024)

Question 23M.3.HL.TZ2.20

Date	May 2023	Marks available	[Maximum mark: 6]	Reference code	23M.3.HL.TZ2.20
Level	HL	Paper	3	Time zone	TZ2
Command term	Determine, Explain, Sketch	Question number	20	Adapted from	N/A

20.

[Maximum mark: 6]

23M.3.HL.TZ2.20

(a)

Determine the critical density of the universe using a Hubble constant value of 73 km s⁻¹ Mpc⁻¹.

[2]

Markscheme

H «= $\frac{73 \times 10^{3}}{3.26 \times 10^{6} \times 9.46 \times 10^{15}}$ » = 2.37 × 10⁻¹⁸ «s⁻¹» ✓

ρ_c = « $\frac{3 \times {(2.37 \times 10^{- 18})}^{2}}{8 π \times 6.67 \times 10^{- 11}}$ =» 1.0 × 10⁻²⁶ «kg m⁻³» ✓

Award [2] for BCA

Allow ECF from MP1

Award [1] for 9.5 × 10¹⁸ or 9.5 × 10¹²

(b)

Sketch, on the axes shown, the variation of R/R₀ (the cosmic scale factor R divided by its present value R₀) with time for a universe where the density is greater than the critical density.

[2]

Markscheme

any irregular semicircular shape that returns to zero ✓

must pass through present and $\frac{R}{R_{0}}$ = 1 ✓

Allow MP2 for any line reasonably going through (present, 1)

(c)

Explain how the presence of dark energy is likely to affect the future rate of temperature change of the universe.

[2]

Markscheme

presence of dark energy accelerates the expansion of the universe ✓

this increases the rate of cooling ✓

Question 23M.3.HL.TZ2.20

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