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Date May 2018 Marks available 2 Reference code 18M.3.SL.TZ1.12
Level Standard level Paper Paper 3 Time zone Time zone 1
Command term Estimate Question number 12 Adapted from N/A

Question

The Hubble constant is accepted to be 70 km s–1 Mpc–1. This value of the Hubble constant gives an age for the universe of 14.0 billion years.

The accepted value of the Hubble constant has changed over the past decades.

The redshift of a galaxy is measured to be z = 0.19.

Explain how international collaboration has helped to refine this value.

[1]
a.

Estimate, in Mpc, the distance between the galaxy and the Earth.

[2]
b.

Determine, in years, the approximate age of the universe at the instant when the detected light from the distant galaxy was emitted.

[3]
c.

Markscheme

experiments and collecting data are extremely costly

data from many projects around the world can be collated

 

OWTTE

[1 mark]

a.

v«zc = 0.19 × 3 × 108 =» 5.7 × 107 «ms–1»

d = «\(\frac{v}{{{H_0}}} = \frac{{5.7 \times {{10}^4}}}{{70}}\)» = 810Mpc     OR     8.1× 108 pc

 

Correct units must be present for MP2 to be awarded.

Award [2] for BCA.

[2 marks]

b.

ALTERNATIVE 1

\(\frac{{{R_{{\text{now}}}}}}{{{R_{{\text{then}}}}}}\) = 1 + z = 1.19

so (assuming constant expansion rate) \(\frac{{{t_{{\text{now}}}}}}{t}\) = 1.19

t = \(\frac{{14}}{{1.19}}\) = 11.7By = 12«By (billion years)»

 

ALTERNATIVE 2

light has travelled a distance: (810 × 106 × 3.26 =) 2.6 × 109ly

so light was emitted: 2.6 billion years ago

so the universe was 11.4 billion years old

 

MP1 can be awarded if MP2 clearly seen.

Accept 2.5 × 1025 m for mp1.

MP1 can be awarded if MP2 clearly seen.

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Option D: Astrophysics » Option D: Astrophysics (Core topics) » D.3 – Cosmology
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