| 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 | Determine | 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.
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.
Markscheme
\(T = \frac{1}{H}{\text{ }}\left( { = \frac{1}{{70{\text{ km}}\,{{\text{s}}^{ - 1}}{\text{Mp}}{{\text{c}}^{ - 1}}}}} \right)\);
\(T = \left( {\frac{1}{{70\,000{\text{ }}{{\text{s}}^{ - 1}}}} \times {{10}^6} \times 9.46 \times {{10}^{15}} \times 3.26 = } \right){\text{ }}4.4 \times {10^{17}}{\text{ s}}\);
\(\left( {\frac{{\Delta \lambda }}{\lambda } = \frac{v}{c}} \right)\)
\(\frac{{\Delta \lambda }}{\lambda } = \frac{{725.6 - 656.3}}{{656}} = 0.106\);
\(v = \left( {\frac{{\Delta \lambda }}{\lambda } \times c = 0.106 \times 3 \times {{10}^8} = } \right){\text{ }}3.17 \times {10^7}{\text{ m}}\,{{\text{s}}^{ - 1}}\);
Examiners report
The majority of candidates answered both questions well.
The majority of candidates answered both questions well.
