## Quantum Numbers

705088777
Posts: 37
Joined: Fri Sep 28, 2018 12:18 am

### Quantum Numbers

Can someone explain how to do quantum numbers (n,l,ml,ms)??

Patrick Cai 1L
Posts: 93
Joined: Fri Sep 28, 2018 12:25 am

### Re: Quantum Numbers

n: the energy level (goes from n = 0,1,2,...)
l: the subshell (goes from l = n-1, n-2,...0)
ml: the orbital (goes from ml = l, l-1,...-l+1,-1)
ms: one of the two electrons that may be within an orbital (either +1/2 or -1/2)

First 3 quantum numbers, when expressed as parameters of the wave function in the form of $\Psi (n, l, m_{l})$, give you a description of an orbital
With the last quantum number, when expressed in the form of $\Psi (n, l, m_{l}, m_{s})$, given you the description of an individual electron

ThomasLai1D
Posts: 61
Joined: Fri Sep 28, 2018 12:17 am

### Re: Quantum Numbers

Hi,

First, you need to determine the energy level, or n. Say the orbital is on the 3rd energy level, so n=3. If n=3, you can determine l, or the angular momentum function (the name is largely irrelevant for finding the number). l is determined by n-1, so the maximum value of l can be n=2, with the possible values of l as 0,1,2. Moreover, 0 corresponds to the s orbital shape, 1 to the p orbital shape, and 2 to the d orbital shape (and 3 to the f orbital shape, but n=3 cannot have an f orbital because the maximum number is n=2. From there, you can find ml, the magnetic quantum number (again, the name is largely irrelevant for finding its value), which is determined as l, l-1 until -l. So if an electron is in the 3p orbital, n=3, l=1, and ml=1,0,-1. The ms value determines the spin, which is either up or down (up = +1/2 and down = -1/2). The ms value is independent of the previous numbers.

Schem_student
Posts: 29
Joined: Fri Sep 28, 2018 12:19 am

### Re: Quantum Numbers

The first thing to understand is that n is the principle quantum number and because items have the same energy they are known to be in the same shell. These shells can be synonymously labeled by the value of n. Next, is the quantum number l which is known as an orbital angular momentum qunatum number and is to equal n-1. But subshells also known as groups of orbitals have the same value of l which is known to be s=0, p=1, d=2, f=3...etc. The next quantum numbers are magnetic quantum numbers ml and ms. ml denotes the specific orbital within a SUBSHELL and ms denotes electron spin of the electron in the specific orbital (possible values +1/2, -1/2).