Question

What is bigger? An atomic orbital or molecular orbital? Why?

Answer 1

An atomic orbital is bigger because in atomic orbitals, only one nucleus is pulling on the electrons so the repulsion between the two electrons in the orbital is higher in relation to nuclear pull than in molecular orbitals. This difference in repulsion allows the electrons to orbit further from the nucleus, thus expanding their probability regions.
Molecular orbitals on the other hand have two nuclei pulling on the electrons which brings them in closer and causes their probability regions to shrink. Smaller orbitals are also more stable than atomic ones, in case you wanted to know.

Answer 2

It depends. There are cases where ArkGoLucky is correct, and atomic orbitals, particularly the most further out (high n, e.g. in heavy transition metals) are larger than molecular orbitals, particularly those in very small tightly bound molecules, like N2.

But in general an MO is larger than an AO, and is well-approximated by the overlap of *several* AOs. (In fact this is often how they are constructed when you do a bonding energy calculation.) The fact that the electrons are attracted to more than one nucleus means, first, that they necessarily spend time near both, which automatically increases the region of space they visit, compared to spending time near just one nucleus. Secondly, having two nuclei means that the electrostatic energy is lowered *without* reducing the distance between nucleus and electron -- because the amount of positive charge has increased.

Indeed, you can look upon the latter effect as one of the main driving forces for chemical bonds: electrons do not "like" to be confined -- their kinetic energy rises steeply when several are confined to a small space, because of the Pauli Principle. From the point of view of an electron, having the positive charge to which its attracted "broken up" into two (or more) chunks -- the two or more nuclei relevant to an MO -- is energetically favorable, because the same electrostatic energy of attraction can be achieved *without* confining the electron close to just one nucleus, which raises the kinetic energy.

Answer 3

Here's some pictures and animations:

http://winter.group.shef.ac.uk/orbitron/