Question #6f111

1 Answer
Nov 7, 2017

Answer:

#"9 electrons"#

Explanation:

The trick here is to realize that you're actually looking for the number of orbitals that are present on the third energy level in a given atom.

This is the case because, as you know, each orbital can hold a maximum of #2# electrons of opposite spins. In other words, for each orbital, you have one electron that has a spin quantum number, #m_s#, equal to #+1/2# and one electron that has a spin quantum number equal to #-1/2#.

Since you're only looking for the number of electrons that have spin-up, you need to take the total number of electrons present per orbital and divide it by #2#. This, of course, gives you the number of orbitals.

As you know, the total number of orbitals present on an energy level described by a principal quantum number #n# is given by

#color(blue)(ul(color(black)("no. of orbitals" = n^2)))#

In your case, you have

#n = 3#

which means that the third energy level can hold a maximum of

#"no. of orbitals" = 3^2#

#"no. of orbitals" = 9#

Since each orbital can hold a single electron that has #m_s = +1/2#, you can say that a total of #9# electrons can have

#n = 3, m_s = +1/2#

in a given atom.