- #1

nv125

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**Electrodynamics and Relativity. Please Help!**

## Homework Statement

Consider the decay of a particle.

(a) Find the threshold kinetic energies of the incident particles in each of

the following reactions:

(i) ∏

^{+}+ p →∏

^{+}+ ∏° + p

(ii) p + n →p + n + ∏° + ∏°

The incident particle is the first particle listed in the reactions; the target particle is at rest. The masses of the ∏

^{+}and ∏° ions are 139.567MeV/c2 and 134.963 MeV/c2 respectively while the masses of the neutron and proton are respectively 939.566 MeV/c2 and 938.272 MeV/c2.

## Homework Equations

The teacher suggested that I will need to use the following equations to get the solution

(Here P is the momentum and Px is the momentum of the incident particle ∏

^{+}in the X direction, assuming it hits the target particle p(proton) horizontally, so no P(momentum) in y or z direction)

ƩP

_{i}

^{u}=0

P

_{u}P

^{u}=m

^{2}c

^{2}= E

^{2}/C

^{2}-P

^{2}

Also said that using this notations will be useful to solve the problem

For ∏

^{+}, the incident particle:

P

_{u}=(E/C, Px, 0, 0)

P

^{u}=(E/C, -Px, 0, 0) where Px is the momentum of the incident particle, and no need to worry about y and z direction so just put zeros.

## The Attempt at a Solution

This is what I have done so far to solve for part i, but I have no clue how to continue.

Since we are solving for the threshold kinetic energy, so assuming that ∏

^{+}, ∏° and p are at rest after the reaction.

(E/C, Px, 0, 0) +(m

_{p}C

^{2}, 0, 0, 0) - (m

_{∏+}C

^{2},0, 0, 0 ) -(m

_{∏°}C

^{2},0, 0, 0 ) - (m

_{p}C

^{2},0, 0, 0 ) = 0

m

_{p}, m

_{∏+}, m

_{∏°}are just the rest mass.

PLEASE PLEASE help me to do this problem! thank you so much!