Practice Redshift in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Redshift is the increase in the observed wavelength of light, usually because a light source is moving away from the observer or because space itself is expanding and stretching the light as it travels.

When light is stretched, it shifts toward the red end of the spectrum.

Showing a random 20 of 50 problems.

Example 1

easy
A red-colored apple is illuminated by white light. Is this an example of redshift?

Example 2

medium
Using v=H0dv = H_0 d with H0=70 km/s/MpcH_0 = 70\text{ km/s/Mpc} and c=3.0×105 km/sc = 3.0\times 10^5\text{ km/s}, find the distance of a galaxy with z=0.02z = 0.02.

Example 3

hard
A spectral line at rest 500 nm500\text{ nm} is observed at 1000 nm1000\text{ nm}. Find zz.

Example 4

easy
A spectral line has rest wavelength 500 nm and is observed at 500 nm. What is the redshift zz?

Example 5

medium
A line at rest 500 nm500\text{ nm} shows recession at 9×106 m/s9\times 10^6\text{ m/s}. Find the observed wavelength.

Example 6

medium
A line at rest 434 nm434\text{ nm} (Balmer Hγ\gamma) is observed at 521 nm521\text{ nm}. Find zz and estimate vv (small-zz approximation).

Example 7

challenge
Using Hubble's law v=H0dv = H_0 d with H0=70 km/s/MpcH_0 = 70 \text{ km/s/Mpc}, a galaxy has z=0.01z = 0.01. Estimate its distance in Mpc (use v≈zcv \approx zc, c=3.0×105 km/sc = 3.0\times10^5 \text{ km/s}).

Example 8

challenge
A photon with rest frequency frest=5.0×1014 Hzf_{rest} = 5.0\times 10^{14}\text{ Hz} is observed from a source at z=0.25z = 0.25. Find the observed frequency.

Example 9

medium
A galaxy recedes at v=1.5×107 m/sv = 1.5 \times 10^7\text{ m/s}. Estimate its redshift zz (small-zz).

Example 10

easy
Redshift usually indicates a light source is moving how relative to the observer?

Example 11

medium
For small redshift, z≈v/cz \approx v/c. A galaxy has z=0.02z = 0.02. Estimate its recession speed.

Example 12

easy
A galaxy shows z<0z < 0. Is the galaxy moving toward or away from us?

Example 13

medium
Two galaxies have z=0.01z = 0.01 and z=0.04z = 0.04. By Hubble's law, which is farther, and by what factor (assuming linear vv-distance)?

Example 14

medium
A spectral line is redshifted with z=0.5z = 0.5. Find the observed wavelength if the rest wavelength is 400 nm.

Example 15

hard
Using v=H0dv = H_0 d with H0=70 km/s/MpcH_0 = 70\text{ km/s/Mpc}, a galaxy is at 200 Mpc200\text{ Mpc}. Estimate its redshift zz.

Example 16

challenge
A quasar shows z=2.0z = 2.0. A line emitted at 121.6 nm (ultraviolet) is observed at what wavelength, and is it now visible?

Example 17

challenge
Using the relativistic Doppler formula 1+z=1+β1−β1+z = \sqrt{\frac{1+\beta}{1-\beta}} with β=v/c\beta = v/c, find zz for β=0.5\beta = 0.5 (3 sig figs).

Example 18

medium
A spectral line shifts from rest 400 nm to observed 440 nm. Find the redshift zz.

Example 19

challenge
A line at rest 656 nm is observed at 1312 nm. Find zz and the observed wavelength's spectral region.

Example 20

medium
Does z>0z > 0 alone tell you the galaxy is moving away because of its peculiar velocity?
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