What is the maximum number of orbitals in an atom that can have the following designations?
(a) 5p
(b) 2pz
(c) n=4
To determine the maximum number of orbitals that can have a specific designation, you need to understand the notation used to represent orbitals.
In the electron configuration notation, the first part represents the energy level (called the principal quantum number, often denoted by "n"), and the second part represents the sublevel (denoted by a letter). The principal quantum number (n) can take any positive integer value, while the sublevel letters signify different types of orbitals.
(a) 5p:
For the p sublevel, there are three orbitals (px, py, and pz). Each orbital can hold a maximum of 2 electrons.
Therefore, for 5p, there are 3 orbitals, and each orbital can accommodate 2 electrons. So, the maximum number of electrons that can be accommodated in 5p orbitals is 3 × 2 = 6.
(b) 2pz:
The pz orbital represents one of the three p orbitals. Similar to the previous case, each p orbital can hold a maximum of 2 electrons. So, the maximum number of electrons that can be accommodated in the 2pz orbital is 2.
(c) n=4:
The notation n=4 represents the energy level (principal quantum number) of 4. In a given energy level (n), there can be several sublevels, and each sublevel can have multiple orbitals. To determine the maximum number of orbitals at a specific energy level, you use the formula 2n², which indicates the number of orbitals that can exist at that energy level.
Using that formula, we can calculate the maximum number of orbitals at n=4:
2 × 4² = 2 × 16 = 32
Therefore, at the energy level (n = 4), the maximum number of orbitals is 32.