What is the very small center core of an atom is called?

The small part in the center of the atom is called a nucleus

The very small center core of an atom is called the nuclues, where the protons and neutrons are located. 

There is one s orbital, and there are three p orbitals, five d orbitals, and seven f orbitals. thus, the answer is b. do not confuse the number of orbitals in a subshell with the number of electrons the subshell can hold. each orbital can hold two electrons, so the capacity of an nf subshell is 14 electrons.