Keep in mind that QED describes what happens, not how it happens. There's nothing in the theory, or any other theory, that describes how an electron converts excess energy into a photon, just that it does.
There is one theory – my
elekton theory – that describes how an
elektron electon makes a photon.
Elektons are photons that hug a nucleus & hence orbit the nucleus.
There is no such thing as an electron (eg a hard little nut) orbiting a nucleus (like the Moon orbiting Earth).
Hence an atom absorbs a photon when the photon becomes an
elektron, ie when the photon is captured by the atom.
And an atom emits a photon when an
elektron breaks free of a nucleus. This is the valence energy orbital stuff.
In essence -- an
elektron (a semi confined photon) becomes a (free) photon when it breaks away from the nucleus (& vice versa). No smoke & mirrors needed.
So, lets look at the OP…….. "We know how an electron makes a photon in an LED. It jump from a higher orbital to a lower one emitting a photon. But in an antenna its occupying the same valence just with a different nucleus each hop. How is the energy transferred to a radio frequency photon?" ......
I answered this yesterday – i said that a radio signal is not made of photons.
An electron or elektron hopping along in or on an antenna from atom to atom would i suppose emit a changing em radiation field, a kind of mini radio signal, but all of thems mini signals would tend to cancel, tending to give zero radio signal.
If the hopping was a forced kind of hopping, eg giving a sinusoidal wave of hopping, then i suppose that the nett radio signal would not be zero – but that signal would be an em radiation, not photons.
A number of posters here have said that there is no real difference between a photon & an em energy packet – but i don’t agree – em radiation is emitted by photons – em radiation is a part of every photon, but a photon is not a part of every em radiation packet.
Actually i can put it another way – a photon is an energy packet, but there is no such thing as an em radiation packet.
[edit][i just realised 2feb2023][if em radiation duznt kum in quantum packets then QED can not help with the math]