law of impulse

*Physicsissuef*

Annihilation (connecting positron and electrons) gives us 2 gamma rays. I.e
[tex]^{0}_{-1}e+ ^{0}_{+1}e \rightarrow 2 \gamma[/tex]
In my textbook says:

Quote by mytextbook

The pair positron-electron is processing according to the laws of preservation of the energy and the impulse...
Impulse of the gamma quant is equal to the both particles, same as the nucleus (which is in interaction with), but, the summary impulse is same before and after the process... That is confirmed in The Wilson's chamber which is inside of magnetic and electric field. In that field the electron and the positron like opposite charged particles are going into opposite directions.

Now my question, what is law of preservation of impulse??
Why [tex]e[/tex] is written like [tex]^{0}_{-1}e[/tex] instead of [tex]e^-^1[/tex] or something??

pam

1. Your text must be translated from one language to another.
I think when it says "preservation of impulse", it just means conservation of momentum.
2. That clumsy notation is what is used in nuclear physics.
It means nucleon number=0. The subscripts are the charge.
That notation is almost never used for simple electrons.

*Physicsissuef*

Quote by pam

1. Your text must be translated from one language to another.
I think when it says "preservation of impulse", it just means conservation of momentum.
2. That clumsy notation is what is used in nuclear physics.
It means nucleon number=0. The subscripts are the charge.
That notation is almost never used for simple electrons.

Yes, I mean conservation of momentum... What is that?

eys_physics

Conservation of momentum means that the total momentum is the same after the reaction as before. For a particle with mass the momentum is

[tex]\textbf{p}=m\textbf{v}[/tex]

where m is the mass and v the velocity of the particle.
For photons:

[tex]|p|=\frac{E}{c}[/tex]

where E is the enery and c the speed of light (in vacuum).

*Physicsissuef*

in this case, it imply for the gamma ray? So
[tex]
|p|=\frac{E}{c}
[/tex] is the one that we look for, right?

eys_physics

Yes in the final state you have two phonons, but in the initial state you have one positron and one electron and they have mass.

*Physicsissuef*

so mv=[itex]\frac{E}{c}[/itex], right?

*Physicsissuef*

and why p is in long brackets i.e |p| ?

*Physicsissuef*

is it same with conservation of energY?

jtbell

Quote by Physicsissuef

and why p is in long brackets i.e |p| ?

Momentum is a vector. It has both magnitude and direction. The vertical bars indicate that we are talking about the magnitude only.

*Physicsissuef*

conservation of energy and conservation of impulse are same in this casE?

malawi_glenn

Quote by Physicsissuef

so mv=[itex]\frac{E}{c}[/itex], right?

No, since the general expression for momentum is related via:

[tex] E^2 = p^2c^2 + m^2c^4 [/tex]

So for massless particles (as the photon):

[tex] P = E/c [/tex]

There is no way that you can get mv = E/c

Quote by Physicsissuef

conservation of energy and conservation of impulse are same in this casE?

Nope.

Conversvation of total energy and conservation of momentum/impulse is not the same thing.

Quote by Physicsissuef

Why [tex] e [/tex] is written like [tex]^{0}_{-1}e [/tex]
instead of [tex]e^-^1[/tex]
or something??

They follow the nuclear notion, as pam pointed out.

*Physicsissuef*

E is energy, so what is the difference?

malawi_glenn

i) momentum is a vector, energy is a scalar.

ii) you have massive particles on the Left Hand Side (LHS) of the reaction.

*Physicsissuef*

So conservation of energy is for the gamma ray, and conservation of momentum for the particles, right?

malawi_glenn

NO

conservation of energy for the whole reaction &
consercation of momentum for the whole reaction!

momentum(LHS) = momentum(RHS)
&
Energy(LHS) = Energy (RHS)

Both equations must be fullfilled.

RHS = right hand side
LHS = left hand side

*Physicsissuef*

And what is conservation of impulse, said with simpler words? Maybe some analogy?

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eys_physics	law of impulse Conservation of momentum means that the total momentum is the same after the reaction as before. For a particle with mass the momentum is [tex]\textbf{p}=m\textbf{v}[/tex] where m is the mass and v the velocity of the particle. For photons: [tex]\|p\|=\frac{E}{c}[/tex] where E is the enery and c the speed of light (in vacuum).

Physicsissuef	in this case, it imply for the gamma ray? So [tex] \|p\|=\frac{E}{c} [/tex] is the one that we look for, right?

malawi_glenn Blog Entries: 9 Recognitions: Homework Help Science Advisor	i) momentum is a vector, energy is a scalar. ii) you have massive particles on the Left Hand Side (LHS) of the reaction.