Question

How many boxes are required to depict the 4f orbitals?

Answer 1

Seven boxes are required to illustrate the 4f orbitals, representing the seven distinct orbitals within the n=4 shell.

Step-by-step explanation:

To depict the 4f orbitals, a total of seven boxes are required. In the context of quantum mechanics and the quantum numbers associated with electron configurations, the fourth principal quantum number (n=4) contains s, p, d, and f subshells. For f-type orbitals, where the azimuthal quantum number (l) is equal to 3, the magnetic quantum number (m₁) can take on seven possible values ranging from -3 to +3, resulting in seven distinct 4f orbitals. Each orbital can be depicted as a box in an orbital filling diagram, meaning seven boxes are hence required to illustrate all the 4f orbitals within the n=4 shell.

Answer 2

Seven boxes are required to depict the 4f orbitals, as the 4f sublevel contains seven unique orbitals based on quantum numbers. Each box represents an orbital that can hold up to two electrons.

Step-by-step explanation:

To answer your question, seven boxes are required to depict the 4f orbitals. In atomic theory, the quantum numbers determine the number of orbitals in a given shell and subshell. For the fourth energy level (n = 4), l can have values from 0 to 3, leading to s, p, d, and f sublevels.

Specifically, for the f-type orbitals where l = 3, the magnetic quantum number ml can be any integer between -3 to +3 inclusive, giving us seven possible values. Each value corresponds to a unique 4f orbital. Therefore, we need seven boxes in an orbital filling diagram to represent the seven 4f orbitals, where each box can hold a maximum of two electrons according to the Pauli exclusion principle.

A filling diagram adheres to Hund's Rule, which states orbitals of equal energy are each occupied by a single electron before any orbital is doubly occupied, and all singly occupied orbitals have electrons with the same spin. This helps to reduce electron repulsion and maintain the lowest energy configuration.