Neutrons In Reactions

[Annemarie]

I have my second year exams for Physics tomorrow and I've got something mixed up in my mind, and I'd really appreciate it if someone could set me straight.

Why is water more effective than lead in slowing down fast neutrons?

Also why do neutrinos interact weakly with material? (Their detection is proof enough that nuclear reactions are taking place, detection units are constructed and then taken under ground so as not to have the weak neutrino signal interferred with by other particles)

 

Cheers. Wish me luck!

[Annemarie]

An absorbing lead sheild of 3 cm thickness reduces the intensity of a narrow beam of gamma rays to 10% of its origonal intensity.

a) Is this process a quantum tunnelling one?

b) What thickness is required to reduce the beam to 0.1% of it's origonal intentisty?

c) What is the half-thickness, reducing the intensity to 50%

d) How much is the intensity reduced if a 5cm thick sheild is used?

e) Given that 10^15 gamma photons are incident, can you specify how thick a lead shield would have to be so that not a ingle gamma photon can pass it?

 

The problem is I know that I have enough knowledge to answer this question, I just can't quite get my head round it. It's funny the things you get mental blocks on.

In quatum tunnelling the amplitude is affected only (i.e. not the wavelngth of the particle), while the particle is "tunnelling" through the barrier it's amplitude decreases exponentially. I also know that intensity is proportional to amplitude squared. But now I'm stuck.

 

Annemarie

[5614]

Why is water more effective than lead in slowing down fast neutrons?

I'm not sure why, but it is! It will be to do with how the neutron interacts with the particles it encounters, sure lead is dense, but that doesn't assure you of the 'correct' in this case we'd want energy reducing collision between barrier and neutron.

 

Also why do neutrinos interact weakly with material?

Neutrinos are electrically neutral so interact via the weak force... they also interact via gravity (as does everything) but their mass is soo small it's effectively totaly undetectable.

 

An absorbing lead sheild of 3 cm thickness reduces the intensity of a narrow beam of gamma rays to 10% of its origonal intensity.

a) Is this process a quantum tunnelling one?

b) What thickness is required to reduce the beam to 0.1% of it's origonal intentisty?

c) What is the half-thickness, reducing the intensity to 50%

d) How much is the intensity reduced if a 5cm thick sheild is used?

e) Given that 10^15 gamma photons are incident, can you specify how thick a lead shield would have to be so that not a ingle gamma photon can pass it?

a) Quantum tunneling could occur but it is not a "quantum tunnelling process"

b) Well I'm guessing that's not a simple as 3-->90% x-->99.9% kinda question, so I don't know!

c) http://jan.ucc.nau.edu/~wittke/Microprobe/Halfthickness.html

d) Again, it this a simple 3->90% so therefore 5->x% ?

e) No I cannot!!! (Maybe 'c' will help)

 

I'm not too sure about 'a' but that's what I think.

 

That's generally not much help, but it's my best!

[Klaynos]

I have my second year exams for Physics tomorrow and I've got something mixed up in my mind' date=' and I'd really appreciate it if someone could set me straight.

Why is water more effective than lead in slowing down fast neutrons?

Also why do neutrinos interact weakly with material? (Their detection is proof enough that nuclear reactions are taking place, detection units are constructed and then taken under ground so as not to have the weak neutrino signal interferred with by other particles)

 

Cheers. Wish me luck![/quote']

 

If I've read and understood your question correctly (which at the moment isn't that likely )

 

Then water is better than lead at SLOWING down neutrons because the probability of an interaction between the neutrons and water molecules is lower than passing through lead so the molecules are more likely to have enough interactions to slow them down in water but not enough to greatly reduce the number that actually continue moving, whereas in lead the neutrons will get stoped instead of just being slowed.

[swansont]

If I've read and understood your question correctly (which at the moment isn't that likely )

 

Then water is better than lead at SLOWING down neutrons because the probability of an interaction between the neutrons and water molecules is lower than passing through lead so the molecules are more likely to have enough interactions to slow them down in water but not enough to greatly reduce the number that actually continue moving' date=' whereas in lead the neutrons will get stoped instead of just being slowed.[/quote']

 

It's actually much more to do with conservation of momentum, from a moderating (slowing down) standpoint.

 

If a mass m elastically strikes another mass m, head-on, it can completely transfer its energy and momentum. Neutrons have very close to the mass of protons in water.

 

If a particle of manss m strikes a particle of mass M, it can only transfer a fraction of its energy. (as practice you should work out what the fraction is) it will go something like (2m/m+M). Since Pb is > 200 times as massive as a neutron, you can only lose a few percent per collision.

 

Of course, not all collisions are head-on, so you don't lose the maximum amount. But this tells you the Pb scattering cross-section would have to be more than 200 times bigger than the proton cross section to be as effective, and it isn't.

[swansont]

An absorbing lead sheild of 3 cm thickness reduces the intensity of a narrow beam of gamma rays to 10% of its origonal intensity.

a) Is this process a quantum tunnelling one?

b) What thickness is required to reduce the beam to 0.1% of it's origonal intentisty?

c) What is the half-thickness' date=' reducing the intensity to 50%

d) How much is the intensity reduced if a 5cm thick sheild is used?

e) Given that 10^15 gamma photons are incident, can you specify how thick a lead shield would have to be so that not a ingle gamma photon can pass it?

[/quote']

 

 

It's not a tunneling process as the term is usually used. Attenuation is from a classical model.

 

Absorption is exponential, so yopu can use I = I₀ 10^-L/L0 where L0 is some characteristic length, like the thickness to reduce to 10%

 

(Or you can use I = I₀ e^-d/d0 - just be consistent )

 

And since it's exponential, can you ever reduce it to zero?

[Annemarie]

I just want to say that today is my last exam, it's High Energy Physics and Astrophysics (and the other exams I've had have been Optical Physics and Spectroscopy, Thermal and Condensed Matter Physics and Electromagnetism and Mechanics), I'm really nervous. But after 5-15 today I will have a year and a half in which I'll be doing some physics work but I'll mainly have a shed load of free time. I'm going to be doing a little bit of work to earn some money, thankfullly I've got a good job with St. John's Ambulance, as one of those peky tabbard people trying to get you to ive your money to help others, but honestly all we want is your money and then you can get on with your lives again! Anyhow, I've been considering lots of different possibilities of what to do with my spare time, I am definatly going to do something to do with physics to enhance my knowledge. I'm also going to learn French and try to advance in my piano playing. It's the nicest feeling in the world knowing that soon you'll have nothing to do, no responsibilities, nothing to worry about. Just free time. *sigh*

So anyway, if anyone has any suggestions let me know.

Also, I always used to use the How Stuff Works forum, now I'm going to adopt this as my new forum home, I think I recognise quite a few names from other forums, espcially Swansont, which can't be a regular name.

Anyhow wish me luck and thankyou again for your help!

[Annemarie]

The law that governs this kind of problem (the intensity problem) is Fick's Law

I=Io e(-uX)

Io- Origonal Intensity I- Final intensity u- Some constant which can be determined when you know two other piece of information, u varies from one material to another X-Length of the shield

[Severian]

Good luck! (Which University are you at?)

[Annemarie]

Hertfordshire

[swansont]

The law that governs this kind of problem (the intensity problem) is Fick's Law

I=Io e(-uX)

Io- Origonal Intensity I- Final intensity u- Some constant which can be determined when you know two other piece of information' date=' u varies from one material to another X-Length of the shield[/right']

 

 

As I recall Fick's Law was for diffusion, not attenuation. flux = -C grad(density) or something like that

[Annemarie]

I hope thats the right equation, but it doesn't really mater if it isn't because it was given in solutions to a piece of coursework, and if thats what my lecturer thinks it is, then if I use a different equation then he would mark it wrong, so I'm going to use it in my exam. I think it is diffusion though, I mean, the gamma rays are diffused by the lead particles. Their intensity is reduced.

[swansont]

I hope thats the right equation, but it doesn't really mater if it isn't because it was given in solutions to a piece of coursework, and if thats what my lecturer thinks it is, then if I use a different equation then he would mark it wrong, so I'm going to use it in my exam. I think it is diffusion though, I mean, the gamma rays are diffused by the lead particles. Their intensity is reduced.

 

 

Gammas don't diffuse, though. Back when I taught reactor physics, I recall Fick's law was applied to neutron diffusion, which explains why neutrons move away from areas with high density (where the fission rate is high, like the center of the core) toward the edge of the core, where the density is lower.

 

Attenuation and diffusion aren't the same, unless we were using some non-standard definitions.

[swansont]

I=Io e(-uX)

 

 

That's Beer's Law

 

(took a little while to recall the name)

[Severian]

I would have called it the exponential attenuation law. I even taught this this year to a first year class - never new it was called 'Beer's Law'!

 

(I thought Beer's law was describing how brain function declines exponentially with beer consumption... (jk))

[swansont]

I would have called it the exponential attenuation law. I even taught this this year to a first year class - never new it was called 'Beer's Law'!

 

(I thought Beer's law was describing how brain function declines exponentially with beer consumption... (jk))

 

 

There's also the fifth law of thermodynamics: beer is good.

[5614]

Or we can have Beer-Lambert law!

 

That's what it's referred to as on wikipedia: http://en.wikipedia.org/wiki/Beer%27s_law