According to the Bohr model of atomic structure (later refined by quantum mechanics into the concept of orbitals), the electrons surrounding the nucleus of an atom are not free to occupy any arbitrary distance or energy value. Instead, they are restricted to certain allowed, discrete regions called electron shells (traditionally labelled K, L, M, N, ... corresponding to the principal quantum number n = 1, 2, 3, 4, ...), each of which corresponds to a specific, fixed amount of energy.

Key characteristics of electron shells include:

• Each shell represents a fixed, quantized energy level — electrons within a given atom can only exist at these specific energies and never at values in between.
• Energy increases progressively with increasing shell number, i.e., E_K < E_L < E_M < E_N ..., meaning electrons in shells farther from the nucleus are held less tightly and possess higher energy.
• Each shell can hold only a limited maximum number of electrons, given by the formula 2n², so the K shell (n=1) holds up to 2 electrons, the L shell (n=2) up to 8, the M shell (n=3) up to 18, and so on.
• Electrons can move from one shell to another only by absorbing a photon of exactly the right energy (to jump to a higher shell) or by emitting a photon of exactly that energy (when falling to a lower shell) — this quantized absorption/emission is the basis for atomic spectral lines.
• Within an atom's overall structure, chemical behaviour is largely determined by the number of electrons in the outermost occupied shell, known as the valence shell.

Given this, "electron shells" are best understood as representing fixed energy levels that electrons are permitted to occupy around the nucleus — the shell number directly reflects the discrete amount of energy associated with electrons residing there.

The remaining statements can be dismissed on this basis: it is well established, both from the Bohr model and from extensive spectroscopic and quantum-mechanical evidence, that electron shells do exist and are a real and useful description of atomic structure; electrons do not all have identical energy values, since electrons in different shells (and even in different subshells within a shell) possess distinctly different energies, which is precisely why atoms have multiple, unequally spaced spectral lines rather than a single one; and electrons do not move randomly without any defined shells, since unrestricted random motion would not produce the sharp, quantized spectral lines and stable atomic structures that are actually observed in nature. Therefore, the correct description is that electrons occupy fixed energy-level shells around the nucleus.