Final answer:
The formula for calculating the total number of electrons at each energy level in an atom is 2n², where n is the principal quantum number of the energy level.
Step-by-step explanation:
The formula to solve for the total number of electrons available at each energy level for an atom is given by 2n², where n represents the principal quantum number or the energy level number. For example, for the first energy level (n=1), the total number of electrons is 2(1)² = 2. As we move to the second energy level (n=2), the formula gives us 2(2)² = 8, meaning there are 8 available slots for electrons. This method of determining electron capacity continues for each subsequent energy level.
In a broader context, the distribution of electrons across various energy levels also considers the Pauli exclusion principle, along with other factors like electron configuration and the Aufbau principle, which dictates the sequence in which orbitals are filled.