The orientation in space of an atomic orbital is associated with

a. the principal quantum number (pi).

b. the angular momentum quantum number (l).

c. the magnetic quantum number (ml).

d. the spin quantum number (ms)

e. none of the above.

Option c. the magnetic quantum number (ml)

Explanation:

The electrons in an atom are identified by four quantum numbers.

The four quantum numbers are:

1) Principal quantum number: n

The principal quantum number (n) tells the main energy level of the electron. This can be any positive integer: 1, 2, 3, 4, 5, 6, 7.

2) Angular momentum quantum number (ℓ)

This second quantum number tells the subshell or kind of orbital. The kind of orbital determines the shape of the orbital.

The value of the angular momentum quantum number (ℓ) may be any integer from 0 to n - 1

n feasible ℓ values

1 0

2 0, 1

3 0, 1, 2

4 0, 1, 2, 3

5 0, 1, 2, 3, 4

The association of the ℓ number and the kind (shape) of the orbital is summarized in this table:

ℓ shape

0 s

1 p

2 d

3 f

3) Magnetic quantum number (mℓ)

The magnetic quantum number (mℓ) tells the orientation in space of an atomic orbital.

The value of the magnetic quantum number (mℓ) depends on the value of the angular momentum quantum number (ℓ). The value of mℓ are from - ℓ to + ℓ.

For example, for ℓ = 2, p orbitals, the possible values of mℓ are - 1, 0, + 1, and they indicate that the p orbitals may be oriented along the x, y or z axis in the space, so you name those orbitals px, py, pz.

Hence, this gives you the correct answer to the question: the orientation in space of an atomic orbital is associated with the magnetic quantum number (mℓ) (option c.)

4) Spin quantum number (s)

Although it is more complex than that, it is understood that the spin quantum number (s) is related to the direction of rotation of the electron in the orbital.