How radio waves create the current in antenna in terms of photons? If it is Compton scattering then why is not changed the freuency of photons?
An elementary explanation, at high school level:
The beam of radio wave photons are coherent, as Vladimir said. Coherent means that the electric and magnetic field of each individual photon has a fixed phase with all the others.
When the wave reaches an antenna, some of the photons are absorbed, pushing the electrons to a slightly higher energy level (energy h*nu) in the conduction band. Thus it is not scattering but absorption that generates the current with the frequency of the incoming beam.
It is coherence that , as the photon is absorbed, pushes or repulses the electrons in step, so that a current that has the frequency of the impinging beam is built up.
No, it is not a Compton scattering - the electrons in antenna are not really free.
A radio wave is a flux of coherent photons, they act together, not one by one.
Any EMW makes charges move but bound charges may make a work, so the incident wave may be partially absorbed.
Besides, a low-frequency Compton scattering is quite the same as the classical EMW scattering. So the "scattered" part of the resulting wave is nearly of the same frequency.
The beam of radio waves with coherent photons may be produced only by MASER. Without that photons do not have correlated phases, e.g. famous 21 cm hydrogen line in radio-astronomy is not consist from coherent photons. For radio waves, produced by usual transmitters situation even “worst” - here there is hardly even to suggest a strict justification to find photons with frequency related with frequency of transmitter. I do not have exact calculations, but to understand the reason of the problem it is enough to recall, that radio-transmitter may emit waves of different shapes and simply described by classical physics, but photon is emitted due to quantum transition between some energy levels and it is very different process. After all, photon by definition is described via time dependent function like $exp(-i\omega t)$ and we may not emit “triangle” photons instead of “sinusoidal” one using transmitter with electric current with tricky time dependance.
Current is moving electrons. A photon with a frequenzy will give its energy to the electrons in the antenna. The energized electrons then travel thru the wire to the radio at the same frequenzy as the photons will give of its energy. When the photon field, or rather the electromagnetic field oscillates from positive+ to negative-, as in the AC used to produce the field, the current in the recieving antenna will also produce current, or moving electrons in a oscillating way, from + to - acording to frequenzy.
The photon to electrons energy "delivery" is due to Einsteins photoelectric effect.