Where does the energy of solar radiation hitting the atmosphere go?
It is broadly true that some solar radiation ends up heating the atmosphere. But it isn't true that the atmosphere absorbs most of the heat emitted by the sun.

Broadly there are several ways that radiation is absorbed:


Some of it (but not much of it) is absorbed directly by certain molecules in the atmosphere (carbon dioxide and water vapour are biggies), directly heating them.
Some of it is reflected by clouds and ice and other parts of the earth and reemitted to space (quite  a lot of it)
Some radiation is absorbed by plants and used to drive photosynthesis (important but not a lot of absorbed radiation)
A lot of it is absorbed by the surface of the earth (land and sea) which is the part that contributes most of the warming effect of sunlight (of course this warmer sea and earth then warms the atmosphere above it either directly be contact or by being absorbed before it is transmitted back into space, though a lot of it is emitted to space).


So, in the end, a lot of the radiation ends up as heat, but mostly via heating of earth and sea not by directly heating the atmosphere. On the other hand, the atmosphere does end up much warmer as a result. And the absorption by the atmosphere does make the difference between the earth being very cold or very habitable as a planet. The details of this are very complicated which is why people build very big computer models when they want to understand global warming which depends of the complicated details of how the atmosphere absorbs fractions of the heat.