Question #f0e05

1 Answer
Jun 22, 2016

Answer:

Here's my take on this.

Explanation:

I assume that you're interested in finding out how many electrons can share those two quantum numbers

#n=4" "# and #" "m_s = -1/2#

The idea here is that you can use the fact that the number of orbitals each energy level can hold is given by the equation

#color(blue)(|bar(ul(color(white)(a/a)"no. of orbitals" = n^2color(white)(a/a)|)))#

Here

#n# - the principal quantum number, the quantum number that gives you the energy level on which the electron resides

In your case, the fourth energy level will have a total of

#"no. of orbitals" = 4^2 = 16#

This tells you that the fourth energy level can hold a total of #16# orbitals. Since each orbital can hold a maximum of #2# electrons, it follows that the maximum number of electrons that can share the quantum number #n=4# is

#"no. of e"^(-) = 2 xx "16 orbitals" = "32 e"^(-)#

Now, half of these electrons will have spin-up, which is given by #m_s = +1/2#, and the other half will have spin-down, which is given by #m_s = -1/2#.

Since you're interested in the number of electrons that have #n=4# and #m_s = -1/2#, you will get

#"no. of electrons" = "32 e"^(-)/2 = color(green)(|bar(ul(color(white)(a/a)color(black)("16 e"^(-))color(white)(a/a)|)))#