# 2 particle system: Photon + Massive particle

1. Jul 29, 2007

### kmarinas86

Consider a two particle system:

---- photon ----------- massive particle ---------------------
------- photon -------- massive particle ---------------------
---------- photon ----- massive particle ---------------------
------------- photon -- massive particle ---------------------
---------------- photon massive particle ---------------------
------------------- photon massive particle ------------------
------------------- photon massive particle ------------------

A photon is emitted and absorbed by a particle. I assume that the massive particle would be pushed in the process, however, when the photon is emitted in the opposite direction:

------------------- photon massive particle ------------------
------------------- photon massive particle ------------------
------------------- photon -- massive particle ---------------
---------------- photon ----- massive particle ---------------
------------- photon -------- massive particle ---------------
---------- photon ----------- massive particle ---------------
------- photon -------------- massive particle ---------------

That's perpetual motion! So it has to be wrong.

The alternative possibility I can think of is this:

As a photon approaches a massive particle which will absorb it, it will (pull it in?)

---- photon ----------- massive particle ---------------------
------- photon -------- massive particle ---------------------
---------- photon ----- massive particle ---------------------
------------- photon -- massive particle ---------------------
-------------- photon massive particle -----------------------

And then when it is emitted, it will pull it out?

-------------- photon massive particle -----------------------
------------- photon -- massive particle ---------------------
---------- photon ----- massive particle ---------------------
------- photon -------- massive particle ---------------------
---- photon ----------- massive particle ---------------------

This seems to be more symmetrical, is this what happens? It certainly isn't perpetual motion. But people tell us of radiation pressure, though solar sails must be reflective.

Alternatively, could the photon be emitted in the other direction:

-------------- photon massive particle -----------------------
-------------- massive particle photon -----------------------
------------ massive particle -- photon ----------------------
------------ massive particle ----- photon -------------------
------------ massive particle -------- photon ----------------

But then this to is perpetual motion. Advice?

2. Jul 29, 2007

### cesiumfrog

It isn't clear what your diagrams are supposed to demonstrate (or rather, they demonstrate something unphysical: the massive particle should continue moving with constant velocity after the event, and not just be shifted to the side briefly), nor why you think this is perpetual motion, but I'd guess that the root of your error is in presuming that the reflected photon has the same frequency as the incident photon.

Can you write down the equations for conservation of momentum?

Last edited: Jul 29, 2007
3. Jul 29, 2007

### kmarinas86

Well the photon has no mass, but it does have momentum. Would that be $p=hf/c$, where $p=momentum$ $h=planck's constant$, $f=frequency$, and $c=speed of light$? We would have then:

$m_i v_i + p_i=m_f v_f + p_f$

Is there supposed to be more than one equation?

4. Jul 29, 2007

### olgranpappy

how about conservation of energy. why don't you tell us a little bit more about your "massive particle." Does it have any internal structure or is it just a point?

5. Jul 30, 2007

### kmarinas86

An Atom.

There are many conservation of energy laws. Also, the outputs are not defined specifically in the problem, so I'm not sure which ones to use.

6. Jul 30, 2007

### olgranpappy

no. there are not. there is one law: Energy is conserved.

In your case you will have to take into account whether or not the atom is left in an excited state.

7. Jul 30, 2007

### cesiumfrog

What you're trying to do is basically derive the Compton Scattering relation, so check out hyper-physics if you're stuck.

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