Energy of neutron in fission reaction

[Magnetic Boy]

Homework Statement

when fission occurs why neutron get less energy as compare to the daughter nuclei? i need both physical and mathematical explanation.

Homework Equations

The Attempt at a Solution

i think it is due to the small mass of neutron. but i am not sure as it is not satisfactory. a neutron may get very high speed to get a significant share of the released energy. but why few MeV?

 

[gneill]

Hint: conservation of momentum.

 

[Magnetic Boy]

i already mentioned there is something to do with mass (hence momentum). i know the fissioned nuclei and neutron can scatter at different angles after fission. and so we get continious spectrum. but my question is why neutron get less energy. as if neutron's mass is low it can get high speed to gain high energy (i already mentioned in the question) but why it's not so?

 

[gneill]

Analyse the simplest case where the fission produces two pieces of mass m and M, where m < M. See how the KE energy must divide if conservation of momentum holds.

 

[Magnetic Boy]

Analyse the simplest case where the fission produces two pieces of mass m and M, where m < M. See how the KE energy must divide if conservation of momentum holds.

sir! according to that formula lower mass should get more energy. neutron is lighter than the fissioned fragments. then why it gets less energy? thanks

 

[gneill]

sir! according to that formula lower mass should get more energy. neutron is lighter than the fissioned fragments. then why it gets less energy? thanks

Show your work! Let's see the math.

 

[Magnetic Boy]

Show your work! Let's see the math.

lighter mass=m
heavier mass=M
energy of mass m=Em
energy of mass M= EM
fission energy=Ef
law of conservation of energy
Ef=1/2m(vm)^2+1/2M(vm)^2 (vm=velocity of mass m)
Ef=(1/2m^2(vm)^2)/m+(1/2M^2(vM)^2)/M
law of conservation of momentum
M(vM)=m(vm)
so
Ef=(1/2m^2(vm)^2)/m+(1/2m^2(vm)^2)/m
Ef=1/2m(vm)^2((m+M)/(Mm))
Ef=Em((m+M)/(M))
we get
Em=Ef(M)/(m+M)
by this logic energy of small fragment will be higher as compare to heavier one. you can check in every experiment data. lighter particle will get more energy.
but why neutron get so little?

Show your work! Let's see the math.

 

[gneill]

lighter mass=m
heavier mass=M
energy of mass m=Em
energy of mass M= EM
fission energy=Ef
law of conservation of energy
Ef=1/2m(vm)^2+1/2M(vm)^2 (vm=velocity of mass m)

Why do you assume that they both have the same velocity? They must have different velocities.

 

[Magnetic Boy]

Why do you assume that they both have the same velocity? They must have different velocities.

i didn't assumed same velocities. i assumed same momentum. which is allowed by law of conservation of momentum

 

[gneill]

i didn't assumed same velocities. i assumed same momentum. which is allowed by law of conservation of momentum

You wrote:

law of conservation of energy
Ef=1/2m(vm)^2+1/2M(vm)^2 (vm=velocity of mass m)

using vm for both masses.

 

[Magnetic Boy]

Why do you assume that they both have the same velocity? They must have different velocities.

sorry, typing mistake. it actually is
Ef=1/2m(vm)^2+1/2M(vM)^2 (vm=velocity of mass m)

 

[Magnetic Boy]

You wrote:

using vm for both masses.

it was just a typo
Ef=1/2m(vm)^2+1/2M(vM)^2 (vm=velocity of mass m, vM=velocity of mass M)
it is a very famous derivation.

 

[gneill]

Okay. My version starts with conservation of momentum. Using M and V for the larger particle, m and v for the smaller:

$MV = mv~~~~$ so that: $~~~~\frac{v}{V} = \frac{M}{v}$

Square both sides:
$\frac{v^2}{V^2} = \frac{M^2}{m^2}$

Form KE ratio:
$\frac{m v^2}{M V^2} \cdot \frac{M}{m} = \frac{M^2}{m^2}$

$\frac{m v^2}{M V^2}= \frac{M}{m}$

$\frac{KE_m}{KE_M} = \frac{M}{m}$

So that as you say the smaller particle should get the larger share of the energy, and your question is why this isn't observed in actual fissions.

I will admit that I am not an expert in nuclear physics. That said, my answer would be that the daughter nuclei (which are typically of similar mass) get the bulk of the KE from the fission (they split the difference in the change in binding energy), and that the escaping neutrons are evolved via their own process that dictates the energy available for them. For example, look up "delayed neutrons" and "prompt neutrons".

 

[Magnetic Boy]

Okay. My version starts with conservation of momentum. Using M and V for the larger particle, m and v for the smaller:

$MV = mv~~~~$ so that: $~~~~\frac{v}{V} = \frac{M}{v}$

Square both sides:
$\frac{v^2}{V^2} = \frac{M^2}{m^2}$

Form KE ratio:
$\frac{m v^2}{M V^2} \cdot \frac{M}{m} = \frac{M^2}{m^2}$

$\frac{m v^2}{M V^2}= \frac{M}{m}$

$\frac{KE_m}{KE_M} = \frac{M}{m}$

So that as you say the smaller particle should get the larger share of the energy, and your question is why this isn't observed in actual fissions.

I will admit that I am not an expert in nuclear physics. That said, my answer would be that the daughter nuclei (which are typically of similar mass) get the bulk of the KE from the fission (they split the difference in the change in binding energy), and that the escaping neutrons are evolved via their own process that dictates the energy available for them. For example, look up "delayed neutrons" and "prompt neutrons".

thanks for the directions. but from where prompt neutron get energy? is it not come from the fission of the neucleus? if neutron get energy share from the fission energy then it should get very high energy. if it not then please clear the point. or refer me a good link about that monstrous energy.

 

[gneill]

thanks for the directions. but from where prompt neutron get energy? is it not come from the fission of the neucleus? if neutron get energy share from the fission energy then it should get very high energy. if it not then please clear the point. or refer me a good link about that monstrous energy.

I don't know enough about the subject to give you an answer with any confidence. What I can suggest is that you open a discussion on the topic in the High Energy, Nuclear, Particle Physics forum.

 

[Magnetic Boy]

I don't know enough about the subject to give you an answer with any confidence. What I can suggest is that you open a discussion on the topic in the High Energy, Nuclear, Particle Physics forum.

OK, thanks for the suggestion and help.