What kind of orbital is designated by the quantum numbers (3,1,1,1/2)? Answer s, p, d, or f only.

n = 3

l = 1 = a p obital
ml</sub = 1
ms = 1/2

To determine the orbital designated by the given quantum numbers (3,1,1,1/2), we need to understand the meaning of each quantum number.

The quantum numbers used to describe an electron's state are the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms).

The principal quantum number (n) describes the energy level or shell in which the electron is located. It can have any positive integer value starting from 1.

The azimuthal quantum number (l) represents the orbital shape. The values of l depend on the value of n and can range from 0 to (n-1). It determines whether an orbital is s, p, d, or f. The corresponding values are 0, 1, 2, and 3, respectively.

The magnetic quantum number (ml) indicates the orientation of an orbital within a subshell. It ranges from -l to +l, including zero.

The spin quantum number (ms) describes the spin orientation of an electron within an orbital. It can have two values, +1/2 and -1/2.

Now, looking at the given quantum numbers (3,1,1,1/2):

The principal quantum number (n) is 3. This means we are in the third energy level or shell.

The azimuthal quantum number (l) is 1. According to the range of values, l = 1 corresponds to the p orbital.

The magnetic quantum number (ml) is 1. Since l = 1, ml can have three values: -1, 0, or +1. Therefore, ml = 1 indicates a specific orientation within the p orbital.

The spin quantum number (ms) is 1/2, representing one of the possible orientations of the electron's spin.

Combining all this information, we find that the orbital designated by the quantum numbers (3,1,1,1/2) is the 2p orbital.

So, the answer is p.