Neutron decay - is my answer unrealistic?

• jeebs
In summary, neutron decay is a natural process in which a neutron transforms into a proton, an electron, and an antineutrino. This process is governed by the weak nuclear force and occurs in unstable and radioactive nuclei. While some theories suggest that neutron decay can occur in a matter of minutes, experimental evidence has shown that the average half-life of a free neutron is around 10 minutes. Therefore, it is not considered unrealistic to expect neutron decay to occur within this time frame. However, further research and studies are needed to fully understand the complexities of this process and its potential implications.
jeebs
Hi,
here's the problem:

"a neutron at rest decays into a proton with a decay energy of 0.78MeV. What is the maximum kinetic energy of the proton left behind?"

here's what I've tried:

In this decay, I assumed that although it's not mentioned, there would be something negatively charged produced to conserve charge. I went with beta decay, so that an electron and an antineutrino would be produced. I assumed that the neutrino was massless and ignored it (my lecturer said it could be ignored).

In the neutron's rest-frame, i said that the proton and electron would have equal and opposite momenta pp and pe respectively, ie.

$$\stackrel{\rightarrow}{p_e} = -\stackrel{\rightarrow}{p_p}$$

ie.

$$p_e = p_p = p$$ (magnitudes are equal.)

Also, for conservation of energy, i said that neutron energy En = Ep + Ee = (mp2 + p2)1/2 + (me2 + p2)1/2 = mn since the neutron has no momentum.

(Here I have used the expression E2 = p2c2 + m2c4 in c=1 units).

mn - (mp2 + p2)1/2 = (me2 + p2)1/2

(mn - (mp2 + p2)1/2)2 = me2 + p2

mn2 - 2mn(mp2 + p2)1/2 + mp2 + p2 = me2 + p2

mn2 + mp2 - me2 = 2mn(mp2 + p2)1/2

hence

$$p = \sqrt{(\frac{m_n^2 + m_p^2 - m_e^2}{2m_n})^2 - m_p^2 }$$

Using wikipedia's data:
mp = 938.272 MeV/c^2
mn = 939.566 MeV/c^2
me = 0.510 MeV/c^2

I get p = 1.188 MeV/c

Again, using E2 = p2c2 + m2c4 I get the proton energy Ep = 938.2727521 MeV and when I subtract the rest energy from this to get the kinetic energy, I am left with 7.52x10-4 MeV.

When I do the same for the electron, I find that Ee is just less than 0.78 MeV.

Is this a reasonable answer? It seems weird to me that the electron should take the vast majority of the energy, especially when I am looking for the maximum PROTON energy?

Thanks.

That's not weird. The electrons rest mass = ~1/1836 of the proton rest mass, so it receives most of the kinetic energy, while the proton has a lot of 'rest' energy. In the problem, 0.78 MeV means the electron is relativistic.

In reality, the neutrino can take a lot of energy/momentum as well, and in beta decay, there is a continuous spectrum of energy with the most probably energy of the beta being ~ 1/3 of the maximum allowable energy.

Hi,

I would like to know more about the beta decay. Could you give me a good reference book to start with? I would like to calculate the electron energy spectrum resulting from a neutron decaying into a proton, electron and anti-electron neutrino. Any idea where to start? Thanks!

quarkmeup said:
Hi,

I would like to know more about the beta decay. Could you give me a good reference book to start with? I would like to calculate the electron energy spectrum resulting from a neutron decaying into a proton, electron and anti-electron neutrino. Any idea where to start? Thanks!
Data for each beta-emitter has been tabulated.

Here is some general information - http://hyperphysics.phy-astr.gsu.edu/Hbase/nuclear/beta2.html
http://hyperphysics.phy-astr.gsu.edu/Hbase/nuclear/beta.html#c5

Decay of a neutron
http://hyperphysics.phy-astr.gsu.edu/Hbase/particles/proton.html#c4

Some notes
http://www.hep.phys.soton.ac.uk/hepwww/staff/D.Ross/phys3002/beta.pdf

Last edited by a moderator:
Thanks! Do you happen to know where I could find the tabulated energy spectrum for decay electrons in the rest frame of the parent neutron?

What is neutron decay?

Neutron decay is the process by which a neutron transforms into a proton, an electron, and an antineutrino. This is a type of radioactive decay that occurs in unstable atomic nuclei.

What causes neutron decay?

Neutrons are made up of quarks, and in some cases, a neutron is unstable and can undergo a process called beta decay. This is when a neutron transforms into a proton, releasing an electron and an antineutrino. This process is caused by the weak nuclear force.

What is the half-life of neutron decay?

The half-life of neutron decay is approximately 10.3 minutes. This means that after 10.3 minutes, half of the original number of neutrons will have decayed into protons, electrons, and antineutrinos.

Is neutron decay a natural or man-made process?

Neutron decay is a natural process that occurs in unstable atomic nuclei. It can also be induced in a laboratory setting using nuclear reactions.

Is my answer unrealistic if I say that neutron decay can create energy?

No, your answer is not unrealistic. Neutron decay does release a small amount of energy in the form of the electron and antineutrino. However, this energy is not significant enough to be used as a source of energy for practical purposes.

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