ANSWERS: 3
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Actually photons are considered waves AND particles- so the have mass, and also don't have mass...
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"massless particle" is a bit misleading. The thing that photons don't have is a "rest mass". But what is "rest mass"? - it is the mass that something would have it it were stationary - and photons are never stationary. Following the theory of Relativigy, mass and energy are interchangable - the mere presence of energy acts like mass - it gravitates and has inertia. "rest mass" is like a sort of residual energy you can't get rid of - but even that may be an illusion and actually due to some sort of internal motion. Most, if not all, of a proton's mass is due to internal motion. Photons DO, however, have momentum and energy. It is their momentum and energy they impart to the matter they collide with. Afterwards, the photon has gone. Photons act like they aren't particles at all, merely a little packet of momentum and energy being transferred between two bits of matter.
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You hqve an excellent question. The underlying principle in the question is that energy has mass, but that is not the case in all circumstances, because of Planck's energy equation, E=hf, hence energy is also frequency. In 1922 Compton fired a photon towards an electron; the electron moved. Calculations showed that the photon had lost energy, a decrease in the frequency, and this lost energy was equal to the amount of energy gained by the motion of the electron. The photon was around post collision, but had less energy. Energy in various forms can and does impart a motive force without that energy having mass.
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