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Date November 2014 Marks available 2 Reference code 14N.3.HL.TZ0.5
Level Higher level Paper Paper 3 Time zone Time zone 0
Command term Estimate Question number 5 Adapted from N/A

Question

This question is about the Hubble constant.

A recent estimate for the value of the Hubble constant is \({\text{70 k}}{{\text{m}}^{ - 1}}{\text{Mp}}{{\text{c}}^{ - 1}}\).

Estimate, in seconds, the age of the universe.

[2]
a.

The wavelength of the lines in the absorption spectrum of hydrogen is 656.3 nm when measured on Earth. Analysis of light from a distant galaxy shows that the same line has a wavelength of 725.6 nm. Determine the recessional velocity of the distant galaxy.

[2]
b.

Markscheme

\(T = \frac{1}{H}{\text{ }}\left( { = \frac{1}{{70{\text{ km}}\,{{\text{s}}^{ - 1}}{\text{Mp}}{{\text{c}}^{ - 1}}}}} \right)\);

\(T = \left( {\frac{1}{{70\,000{\text{ }}{{\text{s}}^{ - 1}}}} \times {{10}^6} \times 9.46 \times {{10}^{15}} \times 3.26 = } \right){\text{ }}4.4 \times {10^{17}}{\text{ s}}\);

a.

\(\left( {\frac{{\Delta \lambda }}{\lambda } = \frac{v}{c}} \right)\)

\(\frac{{\Delta \lambda }}{\lambda } = \frac{{725.6 - 656.3}}{{656}} = 0.106\);

\(v = \left( {\frac{{\Delta \lambda }}{\lambda } \times c = 0.106 \times 3 \times {{10}^8} = } \right){\text{ }}3.17 \times {10^7}{\text{ m}}\,{{\text{s}}^{ - 1}}\);

b.

Examiners report

The majority of candidates answered both questions well.

a.

The majority of candidates answered both questions well.

b.

Syllabus sections

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