Final answer:
The equation to predict the total number of electrons in a shell is 2n². For individual subshells, the equation 2(2l + 1) is used, where 'n' is the shell number and 'l' is the subshell type. This allows prediction of electron distribution in shells and subshells.
Step-by-step explanation:
To predict the total number of electrons in a shell, we use the equation 2n², where 'n' represents the principal quantum number or the shell number. For example, for the first shell (n = 1), the equation 2n² equals 2, which means there can only be two electrons in the first shell. Similarly, for the second shell (n = 2), we apply the same equation resulting in 2n² = 8, indicating that eight electrons can be housed in the second shell.
To further break down the electron distribution into subshells, the formula 2(2l + 1) is used, where 'l' represents the azimuthal quantum number or the subshell type (s, p, d, f, etc.). For instance, in the n = 2 shell, there are two subshells: the 2s (l = 0) and the 2p (l = 1) subshells. Using the formula, the 2s subshell can hold 2(2×0 + 1) = 2 electrons, and the 2p subshell can contain 2(2×1 + 1) = 6 electrons, totaling 8 electrons for the entire n = 2 shell, which is consistent with the 2n² rule.