Can a lamp with a broken light bulb produce electromagnetic radiation?

and

What happens when you have two colored lamps in a dark room. A red one on the left and a green one on the right, and you place your hand in the center of the 2! Would the shadows on the white wall be (from left to right) red, yellow, green???

A broken light bulb can produce infrared electromagnetic radiation, but you can't read by it.

The shadow of the red bulb will be green, and the shadow of the green light will be red.

To answer your first question, a lamp with a broken light bulb cannot produce electromagnetic radiation. The light bulb is the component responsible for emitting light, which is a form of electromagnetic radiation. If the light bulb is broken or not functioning, the lamp will not produce any visible light or electromagnetic radiation.

As for your second question, when you have two different colored lamps in a dark room and place your hand in the center, the resulting shadows on the white wall will not create a mix of colors. The reason for this is that light behaves differently when passing through or interacting with objects of different colored light sources.

In this scenario, the red lamp on the left side will cast a shadow of your hand on the white wall, blocking the red light and creating a dark shadow. The green lamp on the right side will also cast its own colored shadow on the wall, blocking the green light and creating another dark shadow. Since the colors of light from the two lamps are not physically mixing at the location of the shadows, the resulting shadows on the white wall will remain predominantly red and green, rather than forming a mixture of colors like yellow.

The colors of the lamps may interact in other ways, such as reflected light, but the shadows directly cast by the lamps will retain their respective colors.