Explain why hotter air rises in the atmosphere

Hot air rises because when you heat air (or any other gas for that matter), it expands. When the air expands, it becomes less dense than the air around it. The less dense hot air then floats in the more dense cold air much like wood floats on water because wood is less dense than water.

Why it rises is because it is lighter than cold air and cold air is more dense than the hotter air