# Finding the recoil energy of an excited atom when it de-excites

1. Feb 23, 2008

### sadhu

I know that i am commiting some serious errors in this , but just cant notice them
suppose we have to find the recoil energy of an excited atom when it de excites

suppose the total energy of the process is E

an atom will emit a photon on returning to normal state . energy of the photon is....... e

recoil velocity of the atom is v;
mass of the atom is M

Mv+e/c=0.................momentum conservation...........c=velocity of light.initialy the atomis at rest

Mv*v/2 + e=E...........energy conservation

from first equation

v=-e/(Mc)...........(i)

thus recoil energy must come out by substituting v

Me*e/(2*M*M*c*c)

e*e/(2Mc*c)

substituting this in energy conservation equation

e+e*e/(2*Mc*c)=E
e+e*e/(2*Mc*c)-E=0

solving for e;
$$\Delta$$=1+2E/(M*c*c)

whats is the solution ???????

Last edited: Feb 23, 2008
2. Nov 3, 2008

### chbeatbama

Re: recoil

The recoil energy (K) is given as:

$$K = E^{2}_{photon}/2mc^{2}$$

where mc2 describes the rest mass of the particle. mc2 will be of the order 109 to 1011 eV for atoms and nuclei.

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