Chapter 44, Problem 1Q

To determine

To find:

the conservation laws that are violated for an electron to decay into two neutrinos, from a given list of conservation laws.

Answer to Problem 1Q

Solution:

An electron cannot decay into two neutrinos because this decay violates angular momentum, charge and lepton number conservation laws. Also electrons and neutrinos are not baryons, and therefore baryon number conservation law cannot be applied to this decay.

Explanation of Solution

Given:

The list of conservation laws that are given is:

a) Energy

b) Angular momentum

c) Charge

d) Lepton number

e) Linear momentum

f) Baryon number

When you look at this equation

e^-   ν + ν

you will immediately see that the charge, and the lepton number conservation laws are violated. But there are other laws that are violated too.

Let us look at the conservation laws in details:

i. If you look at the angular momentum (spin) both, an electron and a neutrino have spin ½; hence (b) that is angular momentum conservation law is violated.

ii. Neutrinos carry no charge, hence (c) that is charge conservation law is not obeyed.

iii. Lepton number of an electron is +1, and for neutrinos is +1 too, hence (d) that is lepton number conservation law is violated. Even if you consider antineutrino-neutrino pair on the right hand side, the lepton number conservation law will be violated.

iv. Electrons and neutrinos are leptons and not baryons; thus the baryon number conservation law (f) does not come into picture at all.

We cannot say anything about the energy and linear momentum conservation laws because electron anyway does not decay into two neutrinos.

Conclusion

Theoretically, a charge is always conserved and thus electron is a completely stable particle.