How many electrons can be contained in all of the orbitals with n = 4? Answer a. 32 b. 2 c. 8 d. 18 e. 10
The correct answer and explanation is:
Correct Answer: a. 32
The number of electrons that can be contained in all of the orbitals with a given principal quantum number (n) depends on the possible sublevels and orbitals associated with that energy level.
For n = 4, the available sublevels are:
- 4s
- 4p
- 4d
- 4f
Each sublevel contains a specific number of orbitals:
- s sublevel has 1 orbital
- p sublevel has 3 orbitals
- d sublevel has 5 orbitals
- f sublevel has 7 orbitals
Each orbital can hold 2 electrons.
So, the total number of orbitals for n = 4 is:
- 1 (from 4s)
- 3 (from 4p)
- 5 (from 4d)
- 7 (from 4f)
Adding them:
1 + 3 + 5 + 7 = 16 orbitals
Now multiply the total number of orbitals by 2 (since each orbital holds 2 electrons):
16 × 2 = 32 electrons
Thus, the maximum number of electrons that can be contained in all orbitals with n = 4 is 32.
This number includes all the electrons that can occupy the fourth energy level regardless of their sublevel. It follows the general formula for the maximum number of electrons in a shell:
2n²
For n = 4:
2 × (4²) = 2 × 16 = 32 electrons
Understanding this is crucial in atomic structure because it helps determine the electron configuration of elements and how electrons are distributed in an atom’s energy levels. The filling of these orbitals according to the Aufbau principle is essential in explaining the chemical behavior of elements in the periodic table.