Question

(a) What is the number of orbitals with the quantum numbers below?

i) (n = 3)
ii) (n = 3, l = 2)
iii) (n = 2, l = 1, m = -1)

a) i) 9 ii) 5 iii) 1

b) i) 3 ii) 4 iii) 3

c) i) 9 ii) 4 iii) 1

d) i) 3 ii) 5 iii) 3

Answer 1

The quantum numbers (n, l, m) describe the location and properties of electrons in an atom. The subshell is determined by the values of n and l. Each subshell can contain multiple degenerate orbitals.

Step-by-step explanation:

The quantum numbers of shells, subshells, and orbitals help describe the location and properties of electrons in an atom. The three quantum numbers are:

1. Principal quantum number (n): Identifies the shell the electron occupies.
2. Angular momentum quantum number (l): Specifies the subshell the electron occupies.
3. Magnetic quantum number (m): Defines the orientation of the orbital in a subshell.

In the case of the given quantum numbers:

1. a) n = 2, l = 1: The electron is in the 2p subshell.
2. b) n = 4, l = 1: The electron is in the 4p subshell.
3. c) n = 6, l = 1: The electron is in the 6p subshell.

Degenerate orbitals are those with the same energy level (n) and subshell (l). Each subshell can contain multiple degenerate orbitals.

1. The 2p subshell contains three degenerate orbitals.
2. The 4p subshell also contains three degenerate orbitals.
3. The 6p subshell also contains three degenerate orbitals.