Calculate velocity of the fastest neutron inside a 96Mo nucl

  • #1
594
12

Homework Statement


Calculate the velocity of the fastest neutron in a 96Mo nucleus and, based on this, explain whether or not we are safe to consider such nucleons in a non-relativistic way. Hint: first
calculate the Fermi energy.

Homework Equations


Fermi energy from Fermi gas model: https://en.m.wikipedia.org/wiki/Fermi_gas

The Attempt at a Solution


Calculating the Fermi energy using Wolfram:
http://m.wolframalpha.com/input/?i=(hbar^2/(2*1.674929*10^-27kg))((3*pi^2((6*10^43)))/1m^3)^(2/3)

Fermi Energy = 30.3946 MeV

Fermi Momentum = √(2mE)
m: mass of neutron
E: Fermi energy

Fermi Momentum = √(2*939.565*30.3946) = 238.988 MeV/c

Velocity = Fermi Momentum / mass
= 238.988 MeV/c / 939.565Mev/c^2
= 0.2547c

So the fastest neutron in 96Mo is travelling at .2547 * speed of light. Provided my calculation is correct, I'm not sure whether we are safe to calculate them in a non-relativistic way though?
 

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,537
6,434
the fastest neutron in 96Mo is travelling at .2547 * speed of light. Provided my calculation is correct, I'm not sure whether we are safe to calculate them in a non-relativistic way though?
Ultimately it depends on what you are going to calculate and how accurately you need the answer. What does it give for the Lorenz factor? That might be a clue.
https://en.m.wikipedia.org/wiki/Relativistic_speed
 
  • #4
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,537
6,434
I calculated the lorentz factor and got 1.03. I'm not sure if this means we are safe to consider the neutrons as non-relativistic though.

http://m.wolframalpha.com/input/?i=1/sqrt(1-(0.2547^2/1^2))
Yes, that's what I got. Borderline, I'd say. I can only repeat, it depends what question you are trying to answer, which perhaps says it is not safe to ignore it.
 
  • #5
594
12
When you say 'borderline' what do you mean?

https://en.m.wikipedia.org/wiki/Fermi_gas#Relativistic_Fermi_gas

This says "For particles with energies close to their respective rest mass we have to use the equations of special relativity"

Considering the neutrons fermi energy is 30.3946 MeV and it's rest mass is 939.565Mev/c2 we could say its energy isn't close to it's rest mass.
 
  • #6
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,537
6,434
"For particles with energies close to their respective rest mass we have to use the equations of special relativity"
Yes, that is certainly true. But it doesn't say that at only 3% it is safe not to. I'm really not sure.
If I had to gamble, I would opt for saying you do not need to consider relativity.
 

Related Threads on Calculate velocity of the fastest neutron inside a 96Mo nucl

Replies
3
Views
493
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
427
  • Last Post
Replies
0
Views
4K
  • Last Post
Replies
6
Views
6K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
7K
  • Last Post
Replies
5
Views
12K
Replies
2
Views
862
Replies
2
Views
1K
Top