Question #fb349

1 Answer
Jul 18, 2017

Answer:

Here's what I got.

Explanation:

As you know, we can use four quantum numbers to describe the position and spin of an electron in an atom.

I assume that you're fairly familiar with how they work, so I won't go into too much detail here.

figures.boundless.com

So, you know that you must find the sets of quantum numbers that can be used to describe an electron located in the #4d# subshell, i.e. in one of the #5# possible #4d# orbitals.

The number added in front of the subshell tells you the energy level on which the subshell is located, i.e. the value of the principal quantum number, #n#.

In your case, you have the #4d# subshell, so you can say that

#n = 4 -># the fourth energy level

The #d# subshell is described by an angular momentum quantum number, #l#, that takes the value

#l = 2 -># the d subshell

For the #d# subshell, the magnetic quantum number, #m_l#, can take one of five possible values

#m_l = {-2, -1, 0, 1, 2} -># five orbitals in the d subshell

Each value of the magnetic quantum number describes one of the five orbitals present in the #d# subshell.

https://chem.libretexts.org

Finally, each orbital can hold a maximum of #2# electrons of opposite spins, which implies that the spin quantum number, #m_s#, can only take two possible values

#m_s = {-1/2, 1/2} -># two electrons of opposite spins

So, you can say that the #4d# subshell can hold a maximum of

#5 color(red)(cancel(color(black)("orbitals"))) * ("2 e"^(-))/(1color(red)(cancel(color(black)("orbital")))) = "10 e"^(-)#

that can be described using the following sets of quantum numbers--each individual orbital is shown in a different color

  • #n=4, l=2, color(blue)(m_l = -2), m_s = -1/2#
  • #n=4, l=2, color(blue)(m_l = -2), m_s = +1/2#
  • #n=4, l=2, color(purple)(m_l = -1), m_s = -1/2#
  • #n=4, l=2, color(purple)(m_l = -1), m_s = +1/2#
  • #n=4, l=2, color(red)(m_l = 0), m_s = -1/2#
  • #n=4, l=2, color(red)(m_l = 0), m_s = +1/2#
  • #n=4, l=2, color(darkgreen)(m_l = 1), m_s = -1/2#
  • #n=4, l=2, color(darkgreen)(m_l = 1), m_s = +1/2#
  • #n=4, l=2, color(darkorange)(m_l = 2), m_s = -1/2#
  • #n=4, l=2, color(darkorange)(m_l = 2), m_s = +1/2#