Number of Electrons in Shells

Electron Capacity of Atomic Shells

Atoms have electrons arranged in shells (energy levels) around the nucleus. Each shell can hold a maximum number of electrons, determined by its principal quantum number (n).

• Principal Quantum Number (n): Indicates the shell or energy level (n = 1, 2, 3, ...).

• Maximum Number of Electrons in a Shell: The formula to calculate the maximum number of electrons in a shell is:

• Where n is the shell number.

• This formula is derived from quantum mechanics and accounts for the number of orbitals and the two possible spin states for each orbital.

Examples and Applications

• Example: How many electrons can be found in the 7th shell of an atom?

  • Using the formula:

  • For n = 7: electrons

• Practice: How many total electrons can be found in the 6th shell of an atom?

  • For n = 6: electrons

• Practice: An element possesses 4 energy levels. How many total electrons can it theoretically hold?

  • For n = 4: electrons

  • However, if the question asks for the total electrons in all shells up to n = 4, sum the electrons in each shell:

    • n = 1:

    • n = 2:

    • n = 3:

    • n = 4:

    • Total: electrons

  • Additional info: The answer circled in the image is 110, which would be the sum up to n = 7: (but for n = 4, the correct sum is 60). The circled answer may be a typographical error or based on a different context.

Summary Table: Maximum Electrons per Shell

Key Points

• Each shell has a maximum electron capacity given by .

• Electron configuration is important for understanding chemical properties and periodic trends.

• Knowing how to calculate the maximum number of electrons in a shell is essential for predicting element behavior.