Fission of Nucleus Homework Answers

[PhysicStud01]

Homework Statement

I have been working some questions on decay but when i considered these 2 examples, there seems to be a problem

Homework Equations

The Attempt at a Solution

Answer to first one is B while that of the second one is C.

When I considered them separately, the answers seem ok, but looking at both, it seems contradicting.

For the one first, since the nucleus have greater mass, i assume that they have most kinetic energy since this depends on mass.

but for the second one, since TH is heavier, it moves slowly, so most of the kinetic energy goes to the aplha. Hence, answer C.

But this IS contracdicting right? IS there something wrong here?

 

[haruspex]

Homework Statement

I have been working some questions on decay but when i considered these 2 examples, there seems to be a problem
View attachment 78754

Homework Equations

The Attempt at a Solution

Answer to first one is B while that of the second one is C.

When I considered them separately, the answers seem ok, but looking at both, it seems contradicting.

For the one first, since the nucleus have greater mass, i assume that they have most kinetic energy since this depends on mass.

but for the second one, since TH is heavier, it moves slowly, so most of the kinetic energy goes to the aplha. Hence, answer C.

But this IS contracdicting right? IS there something wrong here?

Remember momentum conservation. The relative speeds will be inversely proportional to their masses. Since KE is like mv², half the mass but twice the speed means twice the energy.

 

[PhysicStud01]

Remember momentum conservation. The relative speeds will be inversely proportional to their masses. Since KE is like mv², half the mass but twice the speed means twice the energy.

I know, but then, the answer B for the first one is not ALWAYS true (in fact, this would explain why C is the answer for the 2nd one). the book still says B is the correct answer for the first one

 

[PhysicStud01]

can anyone explain please. from the conservation of momentum, the answer to the first one cannot be B.

 

[haruspex]

I know, but then, the answer B for the first one is not ALWAYS true (in fact, this would explain why C is the answer for the 2nd one). the book still says B is the correct answer for the first one

I'm not following your logic. Why would momentum conservation make B not always true for the first question? How does it limit the ability of the emitted nuclei to carry lots of KE?

 

[PhysicStud01]

I'm not following your logic. Why would momentum conservation make B not always true for the first question? How does it limit the ability of the emitted nuclei to carry lots of KE?

relative to the neutrons and beta emiited, the nuclei have much larger mass. so, their speeds will be much less thank that of neutrons and beta. How them can they ALWAYS have large KE that carry most of the energy?

 

[haruspex]

relative to the neutrons and beta emiited, the nuclei have much larger mass. so, their speeds will be much less thank that of neutrons and beta.

That doesn't follow. All I showed is that for two large mass emitted particles, conservation of momentum means the lighter particle will have the greater energy. If you also have much lighter particles the position is more complex. They could travel quite slowly without requiring much adjustment to the speeds of the heavier particles. On the other hand, there's no obvious reason why those lighter particles can't go at stupendous speeds, taking the lion's share of the energy. One would have to go into into more detailed theory of subatomic processes.
I gather 1MeV is typical for an emitted neutron, but I can't find any theoretical basis discussed for that.

 

[PhysicStud01]

That doesn't follow. All I showed is that for two large mass emitted particles, conservation of momentum means the lighter particle will have the greater energy. If you also have much lighter particles the position is more complex. They could travel quite slowly without requiring much adjustment to the speeds of the heavier particles. On the other hand, there's no obvious reason why those lighter particles can't go at stupendous speeds, taking the lion's share of the energy. One would have to go into into more detailed theory of subatomic processes.
I gather 1MeV is typical for an emitted neutron, but I can't find any theoretical basis discussed for that.

so if I'm doing Al-levels, what could explain why B is correct at my level? and the question says ALWAYS, i believe it should be something quite obvious, right?

does it have to do with one is fission and the other is decay?

 

[haruspex]

one is fission and the other is decay

The two overlap. Unstimulated fission is a kind of decay. Alpha decay is effectively a kind of fission, though usually not described as such.

what could explain why B is correct at my level?

I don't know that you are expected to justify the answer, maybe just know it. (And I don't know the answer - probably involves quantum theory.)

 

[PhysicStud01]

The two overlap. Unstimulated fission is a kind of decay. Alpha decay is effectively a kind of fission, though usually not described as such.

I don't know that you are expected to justify the answer, maybe just know it. (And I don't know the answer - probably involves quantum theory.)

could it be that the speed of the neutrons, beta, .. have limited to the speed of light. so, they have limited energies?

 

[lightgrav]

The 2 big nuclei are repelling each other: huge electric PE at break-up becomes huge KE at large distances. The betas are attracted, so can lose typically 15 or 20 MeV on the way out. (The neutrons and gammas essentially keep their initial KE)

 

[PhysicStud01]

The 2 big nuclei are repelling each other: huge electric PE at break-up becomes huge KE at large distances. The betas are attracted, so can lose typically 15 or 20 MeV on the way out. (The neutrons and gammas essentially keep their initial KE)

electric PE? are the nuclei not neutral, even though they are radioactive? they are nuclei of elements, right or is it only the nucleus that are formed?

 

[lightgrav]

The nucleus is INSIDE the atom's electrons ... an atom is neutral due to collecting all those negative electrons.
A "heavy nucleus" has Z ≈100 protons and even more neutrons ... only the neutrons are neutral.
each proton has charge +e (=1.6E-19C), so if the heavy thing splits in half, both "mid-size" nuclei
have charge 50e and their centers are only 12E-15m apart.
It is the immense (+) electric PE that makes big nuclei unstable.

 

[PhysicStud01]

The nucleus is INSIDE the atom's electrons ... an atom is neutral due to collecting all those negative electrons.
A "heavy nucleus" has Z ≈100 protons and even more neutrons ... only the neutrons are neutral.
each proton has charge +e (=1.6E-19C), so if the heavy thing splits in half, both "mid-size" nuclei
have charge 50e and their centers are only 12E-15m apart.
It is the immense (+) electric PE that makes big nuclei unstable.

OK. Thanks. The explanation is actually simple for A-level.

 

[haruspex]

could it be that the speed of the neutrons, beta, .. have limited to the speed of light. so, they have limited energies?

That doesn't limit the energy. As the speed approaches c, the energy tends to infinity.
Glad lightgrav was able to come up with an explanation. It does leave the question of why the neutrons should have any speed. Maybe that's down to the weak and strong nuclear forces, or maybe the neutrons detach a little after the main break up.

 

[lightgrav]

The neutrons have a lot of momentum (hence KE) when confined in the nucleus.
They're magnetically attracted as they leave, but that will only take away 4 or 5 MeV.

 

[haruspex]

The neutrons have a lot of momentum (hence KE) when confined in the nucleus.

Hmm... I wonder if that knowledge is by working backwards from the speed with which they escape.

 

[lightgrav]

They're confined in a really small space, so (Heisenberg says) have large momenta.
Various neutrons in any specific nucleus have KE and PE that can be calculated (estimated)
via shell model (or simper liquid-drop model, or difficult quark-plasmon model, or ...)
which are verified or tweaked by experiments using magnetic excitations (by probe electrons, especially).
fission after collision is not very consistent in the particular neutrons that get released.