| Date | May 2015 | Marks available | 1 | Reference code | 15M.3.HL.TZ2.5 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 2 |
| Command term | Show that | Question number | 5 | Adapted from | N/A |
Question
This question is about Hubble’s law.
A galaxy a distance d away emits light of wavelength λ. Show that the shift in wavelength Δλ, as measured on Earth, is given by
\[\Delta \lambda = \frac{{{H_0}d\lambda }}{c}\]
where H0 is the Hubble constant.
Light of wavelength 620 nm is emitted from a distant galaxy. The shift in wavelength measured on Earth is 35 nm. Determine the distance to the galaxy using a Hubble constant of 68 km s–1Mpc–1.
Markscheme
combining \(\frac{{\Delta \lambda }}{\lambda } = \frac{v}{c}\) and v=H0d;
Answer given, check working.
(mark is for rearrangement)
d=250(Mpc) or 7.7×1024 (m);
Allow only first marking point if incorrect value for λ is used.
Award [2] for a bald correct answer.
Examiners report
In part (a) there were almost no incorrect answers.
In part (b) far too many candidates lost 1 mark because they used the wrong power of ten for velocity in Hubble’s constant.
