Calculating Average Binding Energy per Nucleon and Decay of Free Neutrons

Click For Summary
SUMMARY

The discussion focuses on calculating the average binding energy per nucleon for Magnesium-26 and the decay of free neutrons. The formula for binding energy is established as Binding E = (Zmp + Nmn - Ma) X 931.494 MeV/u, where Ma represents the mass of the nucleus. Additionally, the decay of free neutrons is analyzed, highlighting that the half-life is 10.4 minutes and the decay can be modeled using the exponential decay formula N(t) = N * e^{-const*t}. Special relativity may not be necessary for the calculations due to the low kinetic energy of 0.0414 eV.

PREREQUISITES
  • Understanding of nuclear physics concepts, specifically binding energy and decay processes.
  • Familiarity with the formula for binding energy, including the roles of atomic number (Z), number of neutrons (N), and mass values (mp, mn, Ma).
  • Knowledge of exponential decay and half-life calculations in nuclear physics.
  • Basic principles of special relativity, although not essential for this discussion.
NEXT STEPS
  • Study the calculation of average binding energy for different isotopes using the binding energy formula.
  • Learn about exponential decay and how to derive the decay constant from half-life data.
  • Explore the implications of special relativity on particle decay and how it affects measurements at relativistic speeds.
  • Investigate the properties of free neutrons, including their decay mechanisms and energy considerations.
USEFUL FOR

Students and professionals in nuclear physics, physicists working on particle decay, and anyone interested in the calculations related to binding energy and neutron behavior.

SteveoFitz
Messages
6
Reaction score
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
 
Physics news on Phys.org
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, N(t)=N*e^{-const*t}.

Find the constant to get the correct half-life (meaning: after t_{half} 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
 
Last edited:

Similar threads

The binding energy per nucleon of tritium
  • · Replies 10 ·
Replies
10
Views
3K
Binding energy per nucleon of the nucleus
  • · Replies 10 ·
Replies
10
Views
3K
Calculating Binding Energy for C13 Neutron Removal
  • · Replies 16 ·
Replies
16
Views
2K
Conceptual question about binding energy, from OCR paper
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Why the binding energy per nucleon has specific pattern?
  • · Replies 2 ·
Replies
2
Views
2K
What is the Binding Energy per Nucleon of 238U in MeV?
  • · Replies 4 ·
Replies
4
Views
3K
Variation in mass and binding energy in nuclear reactions
  • · Replies 5 ·
Replies
5
Views
2K
Calculating Average Binding Energy per Nucleon in Deuterium
  • · Replies 2 ·
Replies
2
Views
3K
Archived Binding energy and deuterium nucleus
  • · Replies 1 ·
Replies
1
Views
6K
Calculate the average binding energy per nucleon
  • · Replies 2 ·
Replies
2
Views
7K