Doppler Shift as Applied to Nuclear Structure and Spectroscopy

[atomicpedals]

Homework Statement

a) Calculate the Doppler shift due to a relative velocity of 3cm/sec.
b) Fine $\Delta E/E$, where $E = 14.4keV$ and $\Delta E$ is the Doppler shift obtained in (a).

Homework Equations

$\frac{f_{0}}{f_{s}}=\frac{c}{c+v_{s}}$

The Attempt at a Solution

So I'm working on the assumption that the non-relativistic Doppler equation I showed above is appropriate (3cm/sec is certainly non-relativistic). So following that I arrive at a Doppler shift of 440Hz. Which would be ~1.8E-12eV assuming $E=fh$. Which makes part (b) 1.25E-16eV. Something seems wrong with my reasoning, but I have no idea what. Have I barked up the wrong tree?

 

[mark726]

Thank you for your post. I can see that you have used the correct equation for calculating the Doppler shift due to relative velocity. However, I believe you may have made a mistake in converting the frequency shift to energy shift. Instead of using E = fh, you should use the equation E = hf, where h is Planck's constant. This will give you a value of 6.2E-14eV for the energy shift, which is equivalent to 0.04% of the original energy of 14.4keV. I hope this helps clarify your confusion. Please let me know if you have any further questions.