How many electrons can fit in the second energy level?

8 electrons would fit in the 2nd energy level.

Electron shell

In chemistry and atomic physics, an electron shell, or a principal energy level, may be thought of as an orbit followed by electronsaround an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on farther and farther from the nucleus. The shells correspond with the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labeled alphabetically with letters used in the X-ray notation (K, L, M, ...).

Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2 (n2) electrons.[1] Since electrons are electrically attracted to the nucleus, an atom's electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a strict requirement: atoms may have two or even three incomplete outer shells. (See Madelung rule for more details.) For an explanation of why electrons exist in these shells see electron configuration.[2]

The electrons in the outermost occupied shell (or shells) determine the chemical properties of the atom; it is called the valence shell.

Each shell consists of one or more subshells, and each subshell consists of one or more atomic orbitals.