Quantam number 

n represents the main energy level and l represents the subshell.

lf n = 4 and l = 3, the subshell is 4f.

In f subshell, there are 7 orbitals and each orbital can accommodate a maximum of two electrons, so, maximum number of elecirons in 4f subshell = 7x 2 = 14

To determine the maximum number of electrons in a subshell, we need to use the formula 2(2l + 1), where l is the azimuthal quantum number (also known as the orbital angular momentum quantum number) and represents the shape of the subshell. The azimuthal quantum number (l) can have integer values ranging from 0 to n-1, where n is the principal quantum number.

In this case, we are given that l = 3 and n = 4.

Substituting the values into the formula:
2(2l + 1) = 2(2*3 + 1) = 2(6 + 1) = 2(7) = 14

Therefore, the maximum number of electrons in the subshell with l = 3 and n = 4 is 14.

Explanation:
- Maximum number of electrons in a subshell is determined by the formula 2(2l + 1).
- For this formula, we are given the values of l = 3 and n = 4.
- Substituting these values into the formula, we find that the maximum number of electrons in the subshell is 14.
- This means that the subshell with l = 3 and n = 4 can accommodate a maximum of 14 electrons.
- The formula 2(2l + 1) is derived from the quantum mechanical principles governing electron configurations.
- The azimuthal quantum number (l) represents the shape of the subshell and can have integer values ranging from 0 to n-1.
- The principal quantum number (n) represents the energy level or shell of the electron.
- By using the formula, we can determine the maximum number of electrons that can occupy a specific subshell based on its shape and energy level.