Question

Determine the maximum number of electrons that can be found in each of the following subshells: \(3 s\), \(3 d, 4 p, 4 f, 5 f\)

Short answer

The maximum number of electrons in subshells 3s, 3d, 4p, 4f, and 5f are 2, 10, 6, 14, and 14, respectively.

Step-by-step solution

Understanding the Subshell Codes

The subshell code corresponds to the azimuthal or orbital quantum number (l). According to quantum mechanics, the subshell s has l=0, p has l=1, d has l=2, and f has l=3.

The number of Orbitals in a Subshell

The number of orbitals in a subshell is determined by the formula \(2l + 1\). So, we can find the number of orbitals for each subshell as follows: 3s (where l=0) has \(2*0+1 = 1\) orbital, 3d (where l=2) has \(2*2+1 = 5\) orbitals, 4p (where l=1) has \(2*1+1 = 3\) orbitals, 4f (where l=3) has \(2*3+1 = 7\) orbitals, and 5f (where l=3) also has \(2*3+1 = 7\) orbitals.

Number of Electrons in Each Subshell

Each orbital can hold up to two electrons, as according to the Pauli exclusion principle. Therefore, the number of electrons in a subshell = number of orbitals * 2. Hence, the 3s subshell can have a maximum of 1*2 = 2 electrons, the 3d subshell can have 5*2 = 10 electrons, the 4p subshell can have 3*2 = 6 electrons, the 4f subshell can have 7*2 = 14 electrons, and similarly, the 5f subshell can have a maximum of 7*2 = 14 electrons.