Redshift & Recession Speed | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

The same pattern appears at longer wavelengths

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Identify redshift by matching a line pattern, not one isolated line. For recession, observed wavelengths are greater than laboratory wavelengths. At non-relativistic speeds, z = Δλ/λ ≈ v/c.

Definition

1 mark

What is meant by redshift?

Model answer: An increase in observed wavelength, or decrease in observed frequency, compared with the known emitted value.

Match several lines; one isolated dark line is not enough.
If the pattern shifts to greater wavelengths, the source is receding in the small-speed model.
Distant galaxies are observed to be redshifted, providing evidence that galaxies are moving apart (9702/41/O/N/24 Q10(a)).

Fractional shift gives recession speed

Use positive changes for a redshift:

\Delta\lambda=\lambda_{\mathrm{observed}}-\lambda_{\mathrm{emitted}}

\Delta f=f_{\mathrm{emitted}}-f_{\mathrm{observed}}

z=\dfrac{\Delta\lambda}{\lambda}\approx\dfrac{\Delta f}{f}\approx\dfrac{v}{c}

Symbols

$z$ = redshift (—)
$\lambda$ = known emitted wavelength (m or nm)
$f$ = known emitted frequency (Hz)
$v$ = recession speed for small redshift (m s⁻¹)
$c$ = speed of light (m s⁻¹)

Worked example

A shifted hydrogen line

A line emitted at 658 nm is observed at 726 nm.

z=\dfrac{726-658}{658}=0.103

v=zc=(0.103)(3.00\times10^8)

Answer

v=3.1\times10^7\ \mathrm{m\,s^{-1}}

Your turnnumerical check

A 500 nm line is observed at 510 nm. Estimate the recession speed.

Show worked answer

v=\dfrac{510-500}{500}(3.00\times10^8)

The estimated recession speed is 6.0 × 10⁶ m s⁻¹.

Common mistake

Use the emitted or laboratory value in the denominator. The observed value belongs only in the change.