What represents the area in an atom where an electron most likely will be found?

An orbital is, more correctly, represented by a wave function or state function, #psi#, which describes a quantum mechanical state.

The probability density, #psi^"*"psi#, rewritten into a radial density distribution #4pir^2R_(nl)^2(r)# (that is, ignoring angular contributions, i.e. from #Y_(l)^(m_l)(theta,phi)#), is often used to describe a radial region of probability in 3D space, about a nucleus, where an electron is most likely to be found.

For example, the radial distance of the highest probability to find a #1s# electron is given at #a_0 = "52.9177 pm"#, since the top of the graph (with a slope of #0#) lines up with #1a_0#.

In organic chemistry one needs to be most familiar with the #s#- and #p#-type orbitals. These orbitals (as with any other orbitals) can be described by using quantum numbers.

For example, the orbitals for the electrons in carbon, and the associated quantum numbers are given below. The nucleus of the carbon atom would reside at the center of the x,y,z coordinate.

Radial and Angular Nodes of Electronic Orbitals