Finding Speed of Neutron after Decay

1. Aug 24, 2015

bob dobilina

1. The problem statement, all variables and given/known data
A Helium 5 at rest decays into Helium 4 and a neutron.
Mass of Helium 4 = 6.648 x 10^-27
Mass of Neutron = 1.67493 x 10^-27
Helium 4 has a momentum of 1.903 x10^-20 and Ek 2.723x10^-14

2. Relevant equations
E=mc^2
v= square root of (E2/m)

3. The attempt at a solution
I have found the mass defect for both Helium 4 and the neutron. and Helium 5.
I think i can use E=mc^2, and then use E in v= square root of (E2/m). I am stuck in trying to figure out what I should use for m? The mass defect on the before or after the decay? Any help appreciated.

2. Aug 25, 2015

haruspex

Hi Bob,

This forum is fairly generic across introductory physics, so, like me, many of those who might help you are not familiar with atomic physics terminology, conventions, and equations. E.g., what is E2? If you could avoid or explain such usages, and post all equations that may be relevant, you are more likely to get help.

3. Aug 25, 2015

bob dobilina

Hello. I will add some clarification

I manipulated the formula for kinetic energy, which is E=(1/2)mv^2
E is energy, m is mass, and v and is velocity.

4. Aug 25, 2015

haruspex

Ah, E2 meant 2Ek, right?
But there are two masses resulting, and they will move at different speeds. For the neutron (at least) that speed may be relativistic, so you might need a post-Newtonian equation for its energy. You'll need to use momentum conservation to pin down the two speeds.

5. Aug 25, 2015

bob dobilina

Yes it means 2Ek. The neutron and He4 move off so their speed would be different. OK, i was unsure if the conservation of momentum law would apply here. I tried to use E=mc^2 to find E, and then inserting E into my formula for v but I think the answer is wrong for the velocity of the neutron...

6. Aug 25, 2015

haruspex

You will need to post all your working if you want anyone to spot where you are going wrong. Preferably, use LaTeX.

7. Aug 25, 2015

William White

have you tried a simple momentum balance?

If the momentum of helium 5 is zero and the momentum afterwards of the helium 4 is given (due to the recoil of ejecting the neutron), you can work out the momentum of the neutron - the sum momentum is conseved.

If you are getting speeds of 10% or more of the speed of light, you might want to use the relativistic momentum equation. But I think the % difference will be not worth worrying about.

8. Aug 25, 2015

NickAtNight

Like this?

$$p_{H4} = p_{n}$$

$$v_{x} = p_{x} / m{x)$$

$$v_{H4} = 2,862,515 v_{n} = 11,361,669$$

No units were given... m is in (kg)? momentum is in (kg-m/s)? for m/s ?

9. Aug 25, 2015

haruspex

Where did you get the 2,862,515 from? If you insist on working with numerics it makes it very hard for others to follow what you are doing. Please learn to do everything symbolically until the final step.
As I posted before, you know the total energy released but it will be shared between the two bodies. You need to use conservation of energy and conservation of momentum to find the two speeds. Create an unknown for each speed and write down the conservation equations. And as I mentioned, you will probably need to use the relativistic energy expression for the lighter body. $\frac 12 m_nv_n^2$ might not be good enough.

10. Aug 25, 2015

William White

The units are SI but don't worry about that yet.

You know (or will make the assumption) that the total momentum is zero.

You know the momentum of the helium 4 as it recoils, so you know

phelium4 + pneutron = 0

11. Aug 25, 2015

NickAtNight

Right, that was the first equation.

Second equation was the classic momentum equation solved for v

He said he had one of the momentums, so it took the provided momentum and divided it by the two masses.

12. Aug 25, 2015

DEvens

Some suggestions:

First, always include your units. You have dropped the units for the He4 momentum. You have dropped the units for the He4 energy. This is vital, since none of the rest of the question makes sense without them.

Make your equations look simple. You wrote E2 and later folks asked you, what is E2. You should have written 2 Ek, or better, $2E_k$.

I look and look, but I do not see anywhere in your problem statement what it is you are meant to determine?

Do a ball-park sitting-down kind of estimate of things to see if you are getting things correct. The He4 is roughly four times the mass of the neutron. So it has to be going roughly one quarter as fast. And since the neutron is going 4 times as fast but has one quarter the mass, it has to have four times the kinetic energy. Roughly.

13. Aug 25, 2015

William White

I look and look, but I do not see anywhere in your problem statement what it is you are meant to determine?

Its in the title "Finding Speed of Neutron after Decay"

14. Aug 25, 2015

DEvens

Indeed. But it is still not in the problem statement where it belongs.

15. Aug 25, 2015

William White

Helium 4 is 2 protons, 2 neutrons, so mass is = 4 amu

neutron mass = 1 amu

Momentum is conserved, so I am expecting that the neutron is going 4x faster than the helium 4, but in the opposite direction. And you know the speed of the helium 4, because you know its momentum

16. Aug 25, 2015

William White

ah! it is not...

17. Aug 26, 2015

bob dobilina

Wow everyone. Really appreciate the help with this one.

Here is a link with the full question and my attempt. There is a lot of info in the question and I am getting thrown off by that tbh.

http://imgur.com/aHxilFE

18. Aug 26, 2015

bob dobilina

Could someone please help me understand by what is meant with " the energy equivalence of the mass defect is observed as an increase in the systems kinetic energy"?

19. Aug 26, 2015

bob dobilina

Yup this is what I tried!

20. Aug 26, 2015

bob dobilina

The next part of question asks me to find the mass of the Helium nucleus.

Last edited: Aug 26, 2015