| 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.
Estimate, in Mpc, the distance between the galaxy and the Earth.
Determine, in years, the approximate age of the universe at the instant when the detected light from the distant galaxy was emitted.
Markscheme
experiments and collecting data are extremely costly
data from many projects around the world can be collated
OWTTE
[1 mark]
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]
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]
