How would you write a full set of quantum numbers for the outermost electron in an Rb atom?

1 Answer
Dec 24, 2015

Answer:

#n=5, l=0, m_l = 0, m_s = +1/2#

Explanation:

Start by writing the complete electron configuration fir a neutral rubidium atom.

Rubidium, #"Rb"#, is located in period 5, group 1 of the periodic table, and has an atomic number equal to #37#. This means that the electron configuration of a neutral #"Rb"# atom must account for a total of #37 # electrons.

#"Rb: " 1s^2 2s^2 2p^6 3s^2 3p^6 3d^10 4s^2 4p^6 color(red)(5)s^1#

So, the outermost electron in a rubidium atom is located on the fifth energy level, in an s-orbital.

As you know, four quantum numbers are used to describe the position and spin of an electron inside an atom.

figures.boundless.com

The principal quantum number, #n#, tells you on which energy level the electron resides. In this case, the outermost electron is located on the fifth energy level, and so #n = color(red)(5)#.

The angular momentum quantum number, #l#, describes the subshell in which the electron resides. For #l#, you have

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

and so on. Since your electron is located in the s-subshell, you will have #l=0#.

The magnetic quantum number, #m_l#, describes the exact orbital in which you can find the electron. For an s-subshell electron, #m_l# can only take one value, #m_l = 0#, since this subshell can only hold one orbital.

Finally, the spin quantum number, #m_s#, describes the spin of the electron. Here you have

  • #m_s = +1/2 -># spin-up electron
  • #m_s = -1/2 -># spin-down electron

For you electron, you can select #m_s = +1/2#. The complete set of quantum numbers that describes this particular electron will be

#n=5, l=0, m_l =0, m_s = +1/2#

The electron is located on the fifth energy level, in the 5s-subshell, in the 5s-orbital, and has spin-up.