Pair Production: Which Conservation Law?

[The Head]

Homework Statement

One of the reasons a single photon could not produce an odd number of electrons and positrons is

a) energy would not be conserved
b) unattainable photon energies would be needed
c) matter would be created
d) charge would not be conserved

Homework Equations

The Attempt at a Solution

This is for AP physics by the way. I would think at first that it would be charge, because logically an odd number would create a charge that doesn't have a net charge of zero. Obviously it isn't B (it can be any energy) or C (matter and energy together are what is conserved). But he has said over and over in class that conservation of energy and momentum is what is important for pair production and this is why there must be a pair. Is some other particle produced and that is why charge is conserved?

 

[Orodruin]

But he has said over and over in class that conservation of energy and momentum is what is important for pair production and this is why there must be a pair.

This is incorrect. Conservation of energy and momentum is why you cannot pair produce in vacuum (you need another external particle to satisfy both). You are correct that producing an odd number would violate charge conservation because there cannot be the same number of positrons and electrons.

 

[ZapperZ]

Homework Statement

One of the reasons a single photon could not produce an odd number of electrons and positrons is

a) energy would not be conserved
b) unattainable photon energies would be needed
c) matter would be created
d) charge would not be conserved

Homework Equations

The Attempt at a Solution

This is for AP physics by the way. I would think at first that it would be charge, because logically an odd number would create a charge that doesn't have a net charge of zero. Obviously it isn't B (it can be any energy) or C (matter and energy together are what is conserved). But he has said over and over in class that conservation of energy and momentum is what is important for pair production and this is why there must be a pair. Is some other particle produced and that is why charge is conserved?

The "energy" part is conserved via the mass of the created particles (i.e. mc²) and the kinetic energies of the particles. So it isn't just the mass content that needs to be accounted for. If the particles all take up the appropriate total kinetic energy, then there should be energy conservation (and momentum conservation as well since those particles are moving).

This means that in the given situation for odd number of electrons+positrons, it will not be impossible for energy and momentum to be conserved. However, it will be impossible for total charge to be conserved.

Zz.