Doppler Shift as Applied to Nuclear Structure and Spectroscopy

In summary, the problem involves calculating the Doppler shift due to a relative velocity of 3cm/sec and then finding the energy shift using the correct equation. The correct value for the energy shift is 6.2E-14eV, which is equivalent to 0.04% of the original energy.
  • #1
atomicpedals
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Homework Statement



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

Homework Equations



[itex] \frac{f_{0}}{f_{s}}=\frac{c}{c+v_{s}}[/itex]

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 [itex]E=fh[/itex]. 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?
 
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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.
 

FAQ: Doppler Shift as Applied to Nuclear Structure and Spectroscopy

1. What is Doppler shift as it applies to nuclear structure and spectroscopy?

Doppler shift refers to the change in frequency of a wave due to the relative motion between the source of the wave and the observer. In nuclear structure and spectroscopy, this phenomenon is used to study the properties of atomic nuclei by analyzing the changes in the energy levels of emitted radiation.

2. How is Doppler shift used to study nuclear structure?

In nuclear spectroscopy, a beam of particles is directed at a target nucleus, causing it to emit radiation. The frequency of this radiation is shifted depending on the velocity of the target nucleus. By measuring the Doppler-shifted frequencies, scientists can determine the energy levels and properties of the nucleus, such as its size, shape, and spin.

3. What is the significance of Doppler shift in nuclear structure and spectroscopy?

Doppler shift is a crucial tool for studying nuclear structure because it allows scientists to gather information about the properties of nuclei that cannot be directly observed. By analyzing the Doppler-shifted frequencies, researchers can gain insights into the internal structure and dynamics of atomic nuclei, which helps in understanding the fundamental laws of nature.

4. How is Doppler shift applied in different types of nuclear spectroscopy techniques?

Doppler shift is used in a variety of nuclear spectroscopy techniques, including gamma-ray spectroscopy, neutron spectroscopy, and X-ray spectroscopy. In gamma-ray spectroscopy, the Doppler shift is used to determine the energy levels and transitions of the nucleus. In neutron spectroscopy, it is used to measure the energies and velocities of neutrons emitted from a target nucleus. In X-ray spectroscopy, Doppler shift is used to study the electronic structure of atoms.

5. What are the challenges of using Doppler shift in nuclear structure and spectroscopy studies?

One of the main challenges of using Doppler shift in nuclear spectroscopy is the need for precise and accurate measurements. The velocity of the target nucleus must be known with high precision in order to accurately determine the Doppler-shifted frequencies. Additionally, Doppler broadening, which is caused by the thermal motion of the nucleus, can complicate the analysis of the spectra. Therefore, careful experimental design and data analysis techniques are essential for obtaining reliable results.

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