The red shift parameter z

Overview

Red shift and blue shift.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   What is meant by red shift?

   Model answer

   Red shift is the observation that the wavelengths in the spectrum of a source are longer than the wavelengths the same source produces in a laboratory, so every line is displaced towards the red end.

2. 2

   What is meant by blue shift?

   Model answer

   Blue shift is the observation that the wavelengths in the spectrum of a source are shorter than their laboratory values, so every line is displaced towards the blue end, which indicates approach.

3. 3

   State the equation for the red shift parameter z, defining each symbol.

   Model answer

   z = Δλ/λ, where Δλ is the change in wavelength between the observed and the laboratory value in metres and λ is the laboratory wavelength in metres, so z has no unit.

4. 4

   State the equation linking the red shift parameter to recession speed, and the condition under which it may be used.

   Model answer

   z = v/c, where v is the recession speed of the source in m s⁻¹ and c is the speed of light in m s⁻¹, and it is valid only where v is much smaller than c.

5. 5

   A line measured at 486 nm in the laboratory appears at 492 nm in the spectrum of a galaxy. Calculate the red shift parameter.

   Model answer

   Δλ = 492 − 486 = 6 nm, so z = 6/486 = 0.0123, and 0.0123 × 486 nm returns the 6 nm shift as observed.

6. 6

   A galaxy has a red shift parameter of 0.0123. Calculate its recession speed.

   Model answer

   v = zc = 0.0123 × 3.00 × 10⁸ = 3.7 × 10⁶ m s⁻¹, and 3.70 × 10⁶ ÷ 3.00 × 10⁸ returns z = 0.0123 as given.

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