What is the maximum number of electrons that could have ml in the principal quantum number n 5?

Postby Victoria_Reimers_3L » Sun Nov 01, 2015 11:27 pm

((Question 3B from the 2007 midterm)) When given the quantum numbers n=5 and ms=+1/2, and asked for the maximum number of electrons that can have these quantum numbers, why would only 25 electrons be able to have these numbers?

Ishwar S. answered • 09/26/18

University Professor - General and Organic Chemistry

n is referred to as the principal quantum number and l is the azimuthal quantum number.

The smallest value n can have is 1. The possible values of l range from 0, 1, 2....(n-1). Since n = 5 in your question, the values of l are 0, 1, 2, 3 and 4.

The value of l tells us the type of orbital that is present. For instance, if

From the value of l, you can get the values of the magnetic quantum number, ml. , which tells us how many subshells are present in that orbital.

s orbital = 1 subshell (ml = 0)

p orbital = 3 subshells (ml = -1, 0, +1)

d orbital = 5 subshells (ml = -2, -1, 0, +1, +2)

f orbital = 7 subshells (ml = -3, -2, -1, 0, +1, +2, +3)

g orbital = 9 subshells (ml = -4, -3, -2, -1, 0, +1, +2, +3, +4)

Since l = 4, we are looking at the g orbital, which contains 9 subshells. Each subshell can hold 2 electrons, therefore, 9 subshells can hold a maximum of 18 electrons.

As you know, each electron has a unique set of quantum numbers that describes its exact location in an atom.

In your case, you are given two qunatum numbers, #n#, the principal quantum number, and #m_l#, the *magnetic quantum number, and are sked to determine how many electrons can share these two quantum numbers in an atom.

The principal quantum number describes the energy level, or energy shell, on which the electron resides. Now, notice that the values the magnetic quantum number can take depend on the value of #l#, the angular momentum quantum number.

For an electron that has #n=5#, #l# can be