Calculating Average Binding Energy per Nucleon and Decay of Free Neutrons

In summary, the conversation involves discussing a question about finding the average binding energy per nucleon of Magnesium-26 and another question about free neutrons decaying while traveling a distance of 12.2 km. The solution for the first question involves using the formula for binding energy, and for the second question, the use of special relativity is suggested, but it may not be necessary. The decay of neutrons is explained to be exponential.
  • #1
SteveoFitz
6
0
Hey guys, simple question about binding energy. I'm asked to find the average binding energy per nucleon of Magnesium-26. Now I thought that I would have to use: Binding E = (Zmp + Nmn - Ma) X 931.494 MeV/u. Where Z is the atomic #, N is the # of neutrons, mp, mn, and Ma are mass of proton, mass of neutron, and mass of nucleus respectively. My question is for Ma would that just be the atomic weight of the atom since it's asking for average binding energy?

Actually I got one more on nuclear physics as well. The questions asks: Free neutrons have a characteristic half-life of 10.4 min. What fraction of a group of free neutrons with kinetic energy 0.0414 eV will decay before traveling a distance of 12.2 km? Do not enter unit. I don't know where to start on this one, we're not given a relationship between these quantities so I'm assuming there's something I'm supposed to interpret from this data.

Anyways, hopefully someone can help thanks!
Steve
 
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  • #2
For the second one, you need to use special relativity. From the energy of the neutron, you can calculate the velocity and thereby the time dilation. Then you just need to figure out how long the neutron takes to travel the 12.2km in its own reference frame.

Edit: Actually, those numbers seem small enough you might not need to use special relativity. If you haven't learned it, don't try to. Just calculate the velocity based on the given kinetic energy.

cookiemonster
 
  • #3


I'm still having problems on this second one, sure i can get the velocity, and then the time using the 12.2 km. However then how am I supposed to find the fraction of neutrons from this data, I'm still perplexed to say the least.
 
  • #4
The decay is exponential: If you have N neutrons at t=0, [tex]N(t)=N*e^{-const*t}[/tex].

Find the constant to get the correct half-life (meaning: after [tex]t_{half}[/tex] there are 50% of the Neutrons left), and then put in the time you found.

I don't think you have to use SRT here, 0.0414eV is not so much
 
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1. What is binding energy per nucleon?

Binding energy per nucleon is a measure of the average amount of energy required to remove a nucleon (proton or neutron) from the nucleus of an atom. It represents the stability of the nucleus and is essential in understanding nuclear reactions and the formation of elements.

2. How is binding energy per nucleon calculated?

Binding energy per nucleon is calculated by dividing the total binding energy of a nucleus by the number of nucleons in that nucleus. The binding energy is determined by subtracting the total mass of the nucleus from the combined mass of its individual nucleons.

3. What does a higher binding energy per nucleon indicate?

A higher binding energy per nucleon indicates a more stable nucleus. This means that less energy is required to break apart the nucleus into its individual nucleons. Elements with higher binding energy per nucleon are more likely to be found in nature as they are able to maintain their stability.

4. How does binding energy per nucleon affect nuclear reactions?

Binding energy per nucleon plays a crucial role in nuclear reactions as it determines whether a reaction will release or absorb energy. Nuclear reactions that result in a decrease in binding energy per nucleon (fusion) will release energy, while those that result in an increase (fission) will absorb energy.

5. What factors affect binding energy per nucleon?

The main factors that affect binding energy per nucleon are the number of nucleons in the nucleus and the type of nucleons present. Generally, nuclei with a higher number of nucleons and a balanced ratio of protons to neutrons (close to 1:1) have a higher binding energy per nucleon, making them more stable.

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