Can anyone help with this question: “Assign 4 quantum numbers to the 3rd, 10th, and 18th electrons in cobalt”?

1 Answer
Nov 28, 2017

Answer:

Here's what I get,

Explanation:

The electron configuration of cobalt is

#"1s"^2color(white)(l) "2s"^2 "2p"^6color(white)(l) "3s"^2 "3p"^6 color(white)(l)"4s"^2 "3d"^7"#

The rules for quantum numbers are

  • #n = 1, 2, 3, 4, …#
  • #l = 0, 1, 2, …, n-1#
  • #m_l = l, l-1, …, 0, …, 1-l, -l#
  • #m_s = ±½#

We fill the orbitals using the Aufbau Principle, Hund's Rule, and tthe Pauli Exclusion Principle.

This gives the following table.

#ulbb("No."color(white)(m)ncolor(white)(m)lcolor(white)(m)m_lcolor(white)(m)m_s)#
#color(white)(ll)1color(white)(mm)1color(white)(ml)0color(white)(m)0color(white)(ml)"+½"#
#color(white)(ll)2color(white)(mm)1color(white)(ml)0color(white)(m)0color(white)(mll)"-½"#

#color(red)(color(white)(ll)3color(white)(mm)2color(white)(ml)0color(white)(m)0color(white)(ml)"+½")#
#color(white)(ll)4color(white)(mm)2color(white)(ml)0color(white)(m)0color(white)(mll)"-½"#

#color(white)(ll)5color(white)(mm)2color(white)(ml)1color(white)(m)1color(white)(ml)"+½"#
#color(white)(ll)6color(white)(mm)2color(white)(ml)1color(white)(m)0color(white)(ml)"+½"#
#color(white)(ll)7color(white)(mm)2color(white)(ml)1color(white)(ll)"-1"color(white)(ml)"+½"#

#color(white)(ll)8color(white)(mm)2color(white)(ml)1color(white)(m)1color(white)(mll)"-½"#
#color(white)(ll)9color(white)(mm)2color(white)(ml)1color(white)(m)0color(white)(mll)"-½"#
#color(red)(color(white)(l)10color(white)(mll)2color(white)(ml)1color(white)(ll)"-1"color(white)(mll)"-½")#

#color(white)(l)11color(white)(mm)3color(white)(ml)0color(white)(m)0color(white)(ml)"+½"#
#color(white)(l)12color(white)(mm)3color(white)(ml)0color(white)(m)0color(white)(mll)"-½"#

#color(white)(l)13color(white)(mm)3color(white)(ml)1color(white)(m)1color(white)(ml)"+½"#
#color(white)(l)14color(white)(mm)3color(white)(ml)1color(white)(m)0color(white)(ml)"+½"#
#color(white)(l)15color(white)(mm)3color(white)(ml)1color(white)(ll)"-1"color(white)(ml)"+½"#

#color(white)(l)16color(white)(mm)3color(white)(ml)1color(white)(m)1color(white)(mm)"-½"#
#color(white)(l)17color(white)(mm)3color(white)(ml)1color(white)(m)0color(white)(mm)"-½"#
#color(red)(color(white)(l)18color(white)(mm)3color(white)(ml)1color(white)(ll)"-1"color(white)(mm)"-½")#

The third, tenth, and eighteenth sets of quantum numbers are marked in red.