This has me stumped! its a tad long but please help me?

an electron of mass m is initially moving with a constant speed v, where v%26lt;%26lt;c. express all algebraic answers in terms of the given quantities and fundamental constants. (A) determin the kinetic energy of the electron (B) determine the de broglie wavelength of the electron


The electron encounters a particle with the same mass and opposite charge (a positron) moving with the same speed in the opposite direction. they undergo a head on collision which results in the disappearance of both particles and production of energy


C) determine the energy of each proton


(d) determine the wavelength of each proton


(e) explain why there must be two photons instead of just one


please help me i don't even know where to start!

This has me stumped! its a tad long but please help me?
First part is simple plug %26amp; chug:


kinetic energy = 1/2 mv^2......since v%26lt;%26lt;c this is OK.





deBroglie wavelenth = h/p (h = Planck's constant, p =momentum which is p=mv for v%26lt;%26lt;c.)





Second part is more work. Incoming energy = mass-energy of 2 electrons plus their kinetic energy. Both e's are moving at the same speed. Add all that up.





The two protons that come out have a certain mass-energy and kinetic energy. That must balance the incoming energy of the 2 electrons. You know the mass-energy of a proton, so you know the amount of KE left for them.





Momentum must be conserved. Total momentum before the collision is ZERO (they are same mass, moving in opposite directions). So total momentum after must also be ZERO - and they're the same mass, so each proton must leave in opposite direction with same velocity (but it will be much slower than the electrons' velocity).





The energy of the proton is its mass-energy plus its KE. Actually the total energy of each proton will equal the total energy of each electron.





Now that you know the proton's velocity you can calculate its deBroglie wavelenth.





Why must there be two protons?


1. Conservation of charge - net charge of electron and position is zero, so one proton must be an anti-proton if the other is a proton.


2. Conservation of energy and momentum - if only one proton was created there would certainly be some leftover energy that would have to then be kinetic energy...but if there is only one particle this would violate conservation of momentum. So there must be two esit particles.


3. Conservation of spin - electrons are spin 1/2 and so are protons - the combo of 2 spin 1/2 particles will total either 0 or 1 spin - but the proton coming out is spin 1/2 so there must be another particle coming out with spin 1/2.





Good luck. Be careful with the units.