# Finding Speed of Neutron after Decay

haruspex
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Formula for momentum is p=mv (m=mass, v= velocity)
p=momentum
Conservation of momentum of law states that total p before reaction = total p after reaction
p before = 0 N (newtons)
p after = (Helium 4 = 1.90306 x 10-20N) + ( momentum of neutron)
Since "total p before must equal total p after ", the momentum of the neutron must be: (-)1.90306 x 10-20N.
If we add the momentum of He4 and of the Neutron after the reaction we get:
(1.90306 x 10-20N) + (- 1.90306 x 10-20N)
= 0
Therefore the laws of conservation of momentum are obeyed.
I manipulated the formula p=mv to solve for velocity, the resulting formula is v=(p/m)
So the velocity of the neutron should be
v=(p/m)
v=(- 1.90306 x 10-20N )/ (1.67493 x 10-27 kg)
v= 1.14x107 m/s

I cant get latex to work on my pc for some reason. Any help would be appreciated at this point. The next part of the question asks to find the mass of the helium 5 nucleus and I am puzzled on that one.
Thanks.
Well, that's not what I asked you to do. I asked you to assign distinct variables to each item and not to plug in any numbers. Never mind, let's press on.
Next we need the total KE of He4 and the neutron. I hope you realise that this is not necessarily just a matter of applying mv2/2. If the speeds are approaching the speed of light then we need to use relativistic equations. So, looking at the speeds you have, do you need to do that here?

Well, that's not what I asked you to do. I asked you to assign distinct variables to each item and not to plug in any numbers. Never mind, let's press on.
Next we need the total KE of He4 and the neutron. I hope you realise that this is not necessarily just a matter of applying mv2/2. If the speeds are approaching the speed of light then we need to use relativistic equations. So, looking at the speeds you have, do you need to do that here?
The question gives me the KE of the He4. The Grade 12 physics course I am taking never talks about relativistic equations...
Speed of light is 3 x 108, according to my data sheet, am i to compare this to the speed of the neutron? Because I am not sure if i have the speed of the neutron correct. Are we still focusing on finding the velocity of the neutron, or the mass of the He5 nucleus?
Thanks,

haruspex
Homework Helper
Gold Member
The question gives me the KE of the He4. The Grade 12 physics course I am taking never talks about relativistic equations...
Speed of light is 3 x 108, according to my data sheet, am i to compare this to the speed of the neutron? Because I am not sure if i have the speed of the neutron correct. Are we still focusing on finding the velocity of the neutron, or the mass of the He5 nucleus?
Thanks,
It is getting close to relativistic speeds, but if you've not been introduced to that aspect then I guess we can ignore it.
We are trying to find the mass of He5. Can you find the total KE of the system after the fission?

Would total KE after fission be equal to KE of He4 plus the KE of the neutron?
To find the KE of the neutron would I be able to just use mv2/2? Since I already found the velocity of the neutron in the previous question?

haruspex
Homework Helper
Gold Member
Would total KE after fission be equal to KE of He4 plus the KE of the neutron?
To find the KE of the neutron would I be able to just use mv2/2? Since I already found the velocity of the neutron in the previous question?
Since we're not worried about relativistic effects, yes.

KE of He5 would be 0 since the problems states it at rest before the reaction.
KE of He4 is given to us.
KE of Neutron could be found using KE=mv2/2. The mass is given to us in the question, and we already found velocity.
Ok, so what do i do when I found the KE? Am i going to be using E=mc2?

haruspex
Homework Helper
Gold Member
KE of He5 would be 0 since the problems states it at rest before the reaction.
KE of He4 is given to us.
KE of Neutron could be found using KE=mv2/2. The mass is given to us in the question, and we already found velocity.
Ok, so what do i do when I found the KE? Am i going to be using E=mc2?
Yes.

Yes.
Could I use the total kinetic energy to find the mass defect by manipulating e=mc2? If so, once I find the mass defect, can I add that mass to the mass of He4 and the neutron to get the mass of He5?

haruspex