Critical radius for nuclear reactions

In summary, the critical radius for nuclear reactions is the size of a sample sphere that will maintain a controlled reaction with vq=1. The author explains that this radius can be obtained by deriving the average path length before a neutron fission reaction occurs, which is 0.079m. However, this does not mean that every neutron produced at the center will undergo one fission reaction, as other fission processes can also occur. Integration is necessary to get the average number of fission reactions from a fission reaction, and this explains why the critical radius is not a fraction of 0.079m as one might expect.
  • #1
Decimal
75
7
Hello!

I am taking a course in nuclear physics using the book An Intro to the Physics of Nuclei & Particles by Dunlap. I am a little confused by an explanation related to the critical radius for nuclear reactions.

The author first defines a value ##vq## as the average number of neutrons produced by a free neutron in a sample of U-235. Here ##v## is the number of neutrons produced in a fission reaction and ##q## is a factor < 1 to account for the neutron loss in the sample. To obtain a controlled reaction in which the number of neutrons remains constant ##vq## should equal ##1##. This I understand. The book derives that for a typical value ##v = 2.5## one should aim for ##q = 0.4##.

My confusion starts when the author explains how one might obtain such a q value. The author derives the average path length before a neutron fission reaction occurs to be equal to ##0.079## m. Then he states that a sample sphere with this radius will be just the right size to keep the reaction controlled (##vq = 1##), also called the critical radius. However in my understanding this means that every neutron produced at the center will undergo on average 1 fission reaction, and thus ##q \approx 1##. Then the reaction would obviously be unstable.

Thus I would think the critical radius would be some fraction of ##0.079## m, related to the q value one would aim for. However this is apparently not the case, so what am I missing? I feel like I am misunderstanding the probabilities involved, but some pointers would be greatly appreciated.

Thanks!
 
Physics news on Phys.org
  • #2
Decimal said:
However in my understanding this means that every neutron produced at the center will undergo on average 1 fission reaction
That would mean no neutron can escape, that is not realistic. In addition neutrons are not only produced at the center. Fission processes elsewhere will on average have more neutrons escaping.

You'll need integration to get the average number of fission reactions from a fission reaction.
 
  • #3
mfb said:
That would mean no neutron can escape, that is not realistic. In addition neutrons are not only produced at the center. Fission processes elsewhere will on average have more neutrons escaping.

You'll need integration to get the average number of fission reactions from a fission reaction.

Right, that makes a lot of sense! Thank you!
 

1. What is the critical radius for nuclear reactions?

The critical radius for nuclear reactions is the minimum distance at which a nuclear reaction can be sustained. It is the point at which the rate of neutron production is equal to the rate of neutron loss, resulting in a self-sustaining chain reaction.

2. How is the critical radius calculated?

The critical radius is calculated using the neutron diffusion equation, which takes into account factors such as the amount of fuel present, the geometry of the fuel, and the properties of the surrounding materials. It is also dependent on the type of nuclear reaction being considered.

3. What factors can affect the critical radius?

Several factors can affect the critical radius, including the amount and type of fuel, the geometry of the fuel, the presence of moderators and neutron absorbers, and the temperature and pressure of the system. Any changes to these factors can alter the critical radius and potentially affect the sustainability of the nuclear reaction.

4. How does the critical radius relate to nuclear safety?

The critical radius is an important factor in nuclear safety as it determines the minimum distance between nuclear fuel and other materials that are necessary to maintain a safe and controlled nuclear reaction. If the critical radius is not maintained, the reaction could become unstable and lead to a nuclear accident.

5. Can the critical radius be changed?

Yes, the critical radius can be changed by altering the factors that affect it, such as the amount and type of fuel, the presence of moderators and neutron absorbers, and the temperature and pressure of the system. However, any changes must be carefully considered and controlled to ensure the safety and stability of the nuclear reaction.

Similar threads

  • High Energy, Nuclear, Particle Physics
Replies
11
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
5
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
17
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
12
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
20
Views
2K
  • Science Fiction and Fantasy Media
Replies
11
Views
523
  • High Energy, Nuclear, Particle Physics
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
7
Views
2K
Back
Top