Calculating Average Binding Energy per Nucleon and Decay of Free Neutrons

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Homework Help Overview

The discussion revolves around calculating the average binding energy per nucleon for Magnesium-26 and analyzing the decay of free neutrons. The original poster seeks clarification on the binding energy formula and how to approach the decay problem involving kinetic energy and distance traveled.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to clarify whether the atomic weight can be used as the mass of the nucleus in the binding energy calculation. They also express uncertainty about how to relate the given kinetic energy of free neutrons to their decay over a specified distance.
  • Some participants suggest using special relativity to calculate the velocity and time dilation for the neutron decay problem, while others question whether this approach is necessary given the small kinetic energy value.
  • One participant notes the exponential nature of decay and provides a formula to relate the initial number of neutrons to the remaining amount after a certain time, prompting further inquiry about how to determine the fraction of neutrons that decay.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problems. Some guidance has been offered regarding the decay formula and the potential relevance of special relativity, but there is no explicit consensus on the best approach to take for either problem.

Contextual Notes

Participants are navigating constraints such as the lack of direct relationships between the given quantities in the decay problem and the original poster's uncertainty about the appropriate use of atomic weight in the binding energy calculation.

SteveoFitz
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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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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
 


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.
 
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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