What happens if we connect a led to a monopole antenna?(on a transmitting antenna)
A diode attached to an antenna plus tuned LC circuit is the basis of the simplest possible radio: http://sci-toys.com/scitoys/scitoys/radio/homemade_radio.html

But the amount of energy available is tiny. It wouldn't be a visible glow, it would be at best something that you could just about detect with sensitive instruments.

Edit: OK, a transmitting antenna! My antenna theory is a little rusty, but I think the best way is to start by understanding a transmission line. Wires are not the simple objects of pure theory; between every conductor and the corresponding ground is a capacitance. We can consider the capacitance divided into little pieces for each corresponding tiny piece of wire segment. When a changing signal enters a wire, it has to fill up all the little capacitances along the way.

The antenna connected to an AC signal has a electric field wavefront travelling up it; when the wave enters it doesn't "know" that there's nothing on the end of the antenna. It reflects off the end of the antenna, and then if the antenna is designed correctly forms a standing wave in the antenna.

So what happens if you stick an LED in the way? I think the diode property stops this working, because it only allows current flow in one direction. You charge up the (tiny) capacitance of the antenna, and then it's full and no more current will flow at that voltage.