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My question is even though photons have no (rest) mass, do they emit a external force due to EM radiation causing electrons to be excited and jump to higher energy shells which electrons have mass thus photons can emit a kinetic force? I am new so I would like to get the record straight on this issue.

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Essentially a duplicate/variation of this Phys.SE question and links therein. –  Qmechanic Mar 5 '13 at 20:23
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They do: see radiation pressure.

Photons have momentum, even in classical electromagnetism, and so they can apply force to particles. In quantum mechanics, the force per photon is $\hbar k$, where $\hbar = h/2\pi$ is the reduced Plank's constant and $k=2\pi/\lambda$ is the wavevector. This force shows up in many situations. For instance, in my experiments, the momentum kicks from photons scattering off atom can push and even cool the atoms. The effect can be substantial: rubidium atoms can be accelerated by $10^4$ m/s${}^2$ by spontaneously scattering light (a momentum kick $\hbar k$ on a mass $m$ at a rate $\Gamma$ gives an acceleration $a = \Gamma \hbar k/m$, where in this case $m=1.4\times 10^{-25}$ kg, $\Gamma = 19$ MHz, and $k=8.1\times 10^6$/m).

In contrast, the effect of light scattering off massive mirrors is much smaller, but has been measured in sensitive experiments. This effect is of paramount importance in gravity wave detection, e.g. LIGO, where the slight change in distance between two mirrors could be a signal of gravity waves. The pressure exerted by the light on the mirrors must be understand and in some situations limits experiments.

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Photons can exert force on matter, a phenomenon known as radiation pressure. However it is not the kinetic energy of a photon which excites atomic electrons into higher orbits. Instead the photon has a certain energy E=hv (where v is the frequency), when a photon with an energy corresponding to the energy difference between one 'orbit' and another is absorbed by the atom it will excite that electron to a higher level instantaneously ( a quantum transition), once in this excited state, the atom can spontaneously de-excite by releasing a photon with the same energy once again returning to the lower energy state. The instantaneous transition is know as a quantum jump or leap and cannot be explained by classical physics. The noble prize for physics last year was awarded partially for witnessing these quantum jump.

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i mean when the electrons jump to higher energy states doesn't the magnetic attraction to the nucleus slightly push the nucleus in one direction causing a "slight" kinetic force or is that the electron technically exerting the kinetic force? –  jake Mar 5 '13 at 20:39
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