What are the quantum numbers for electrons in the #4d# orbitals?

1 Answer
Sep 27, 2017

Answer:

Here's what I got.

Explanation:

As you know, the principal quantum number, #n#, tells you the energy shell in which the electron is located.

In your case, the electron is said to occupy the #"4th"# energy level, which is equivalent to saying that it is located in the #"4th"# energy shell, so

#n = 4#

The angular momentum quantum number, #l#, tells you the energy subshell in which the electron is located. For this quantum number, you have

  • #l = 0 -># the #s# subshell
  • #l = 1 -># the #p# subshell
  • #l = 2 -># the #d# subshell
    #vdots#

and so on. In your case, you have

#l = 2#

Now, the #d# subshell can hold a maximum of five #d# orbitals, which are denoted by the values of the magnetic quantum number, #m_l#.

For the #d# subshell, you have

#m_l = {-2, -1, 0, 1, 2}#

Finally, the spin quantum number, #m_s#, which denotes the spin of the electron, can take two possible values

#m_s = {+1/2, - 1/2}#

You now have all the information that you need to write the sets of quantum numbers that can describe an electron located on the #"4th"# energy level, in the #4d# subshell.

I'll show you four sets to start you off

  • #n = 4, l =2, m_l = -2, m_s = +1/2#
  • #n = 4, l = 2, m_l = 0, m_s = -1/2#
  • #n = 4, l =2, m_l = 1, m_s = -1/2#
  • #n = 4, l =2, m_l = 1, m_s = +1/2#