neutron and a proton collide...

[dg2008]

Question

 

A neutron and a proton collide with a kinetic energy of 150 MeV. You may assume that a neutron and a proton each have the same mass energy. Given that a pion has a mass energy of 140 MeV, which of the following reactions are allowed and which are not allowed?

 

n + p → p + p + π–

n + p → n + p + π+ + π–

n + p → n + n + π0

n + p → n + n + π+ + π–

 

Reaction allowed? If not is it due to Energy conservation &/or Charge

conservation

 

I had thought that the middle two were allowed

 

How do I work out the conversions?

[swansont]

If you have 150 MeV of kinetic energy, you are limited to 150 MeV of mass energy in the products. How can you get more than one pion from that?

 

Also look at the charge — you have +1 unit of charge in the reactants, so you'd better have +1 in the products.

[dg2008]

so:

 

n = 0 charge

p = +e charge

 

n + p → p + p + π– = 0 + e → + e + e + -e = 1e

 

n + p → n + p + π+ + π– = 0 + e → 0 + e + e + -e = 0

 

n + p → n + n + π0 = 0 + e → 0 + 0 + 0 = 0

 

n + p → n + n + π+ + π– = 0 + e → 0 + 0 + e + -e = 0

 

so the first one is the only one that could work. 3rd due to energy, 4th due to both energy & charge, or am i completely wrong

Edited March 27, 2009 by dg2008

[lakmilis]

the first two give +1 , latter two give 0.

 

2nd one violates mass energy no?

[swansont]

the first two give +1 , latter two give 0.

 

2nd one violates mass energy no?

 

Right. #2 conserves charge but not energy.

[timo]

Being pedantic one should say "can conserve", not "conserves" (for energy).

[swansont]

Being pedantic one should say "can conserve", not "conserves" (for energy).

 

OTOH, if it's a real reaction, it conserves energy. (Can happen vs did happen)

[timo]

The charge degree of freedom is fixed with giving the reaction partners. The kinetics (strictly speaking also the reaction mechanism) is not fixed. There are kinetic configurations for the process (say all for which the muon gets 3 GeV kinetic energy) which would violate energy conservation and hence do not occur in nature. You implicitly claimed that if the sum of the masses of the reactants and their kinetic energies is at least as high as the sum of the masses of the products then the reaction can occur. This assumption is true in the cms system and only in the cms system. I am not sure to what extent this frame-dependence is obvious to everyone.

In short: I thought I should give a hint that a reaction of course also must conserve momentum.

[Lan(r)12]

this is some crazy stuff lol

[lakmilis]

good point atheist