Answer to Question #109315 in Quantum Mechanics for DD

Question #109315
The frequency of the light emitted by a galaxy receding from the earth is measured
to be (1.5×10^3) MHz. Assuming that the wavelength of the light source is 22.5 cm,
calculate how fast the galaxy is receding from the earth?
1
Expert's answer
2020-04-15T10:25:50-0400

The frequency of a stationary galaxy is


f0=cλ0.f_0=\frac{c}{\lambda_0}.


Write the equation for Doppler effect:


f=f01vrc= vr=(1f0f)c=(1cfλ0)c= =(131081.51090.225)3108=33.3106 m/s==0.111c.f=\frac{f_0}{1-\frac{v_r}{c}}=\\ \space\\ v_r=\bigg(1-\frac{f_0}{f}\bigg)c=\bigg(1-\frac{c}{f\lambda_0}\bigg)c=\\ \space\\ =\bigg(1-\frac{3\cdot10^8}{1.5\cdot10^9\cdot0.225}\bigg)3\cdot10^8=33.3\cdot10^6\text{ m/s}=\\ =0.111c.


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