Electronic Structure: Number of Electrons: Videos & Practice Problems

The maximum number of electrons in an electron shell can be determined using the formula $2n^2$, where $n$ is the principal quantum number of the shell. For example, for the first shell ($n$ = 1), the maximum number of electrons is $21^2=2$. For the second shell ($n$ = 2), it is $22^2=8$. This formula helps in understanding the electron configuration and the structure of atoms.

The electron capacity of the third shell in an atom can be calculated using the formula $2n^2$, where $n$ is the principal quantum number. For the third shell, $n$ = 3. Therefore, the maximum number of electrons it can hold is $23^2=18$. This means the third shell can accommodate up to 18 electrons.

The formula $2n^2$ is used to determine the number of electrons in a shell because it accounts for the quantum mechanical principles governing electron distribution. The principal quantum number $n$ indicates the shell level, and the formula incorporates the number of possible subshells and orbitals within that shell. Each orbital can hold a maximum of 2 electrons, and the formula ensures that all possible orbitals are considered, providing an accurate count of the maximum electron capacity for each shell.

The fourth shell in an atom can hold a maximum number of electrons determined by the formula $2n^2$, where $n$ is the principal quantum number. For the fourth shell, $n$ = 4. Therefore, the maximum number of electrons it can hold is $24^2=32$. This means the fourth shell can accommodate up to 32 electrons.

The principal quantum number ($n$) is significant in electron configuration as it indicates the main energy level or shell of an electron within an atom. It determines the size and energy of the shell, with higher $n$ values corresponding to shells that are further from the nucleus and have higher energy. The principal quantum number also helps in calculating the maximum number of electrons a shell can hold using the formula $2n^2$. Understanding $n$ is crucial for grasping the arrangement of electrons in atoms and their chemical properties.