How many electrons in an atom can have the n = 5, l = 2 designation?

1 Answer
Stefan V.
Dec 24, 2016

#"10 electrons"#

Explanation:

All you really need in order to answer this question is a version of the Periodic Table of Elements that shows the blocks

http://allfactsperiodictable.blogspot.ro/

Now, the principal quantum number, #n#, gives you the energy level on which the electron is located. This is equivalent to the period in which the element is located in the Periodic Table.

In your case, #n=5# designates an element located in period #5#.

Next, the angular momentum quantum number, #l#, tells you the subshell in which the electron resides. The subshells are equivalent to the blocks of the Periodic Table.

You have

  • #l=0 -># the s subshell #=# the s block
  • #l=1 -># the p subshell #=# the p block
  • #l=2 -># the d subshell #=# the d block
  • #l=3 -># the f subshell #=# the f block

In your case, #l=2# designates an electron located in the #d# block of the Periodic Table.

Now, the #d# block contains a total fo #10# groups, i.e. #10# columns of the Periodic Table. Each group is equivalent to #1# electron. This means that the #d# block, which is equivalent to the #d# subshell, can hold a total of #10# electrons.

Therefore, a maximum of #10# electrons can share the two quantum numbers

#n=5, l=2#

These electrons are located on the fifth energy level, in the d subshell, i.e. in one of the #5# d orbitals shown below

http://chemistryjee.blogspot.ro/2015/08/crystal-field-theory.html

As a side note, you can find the number of orbitals that can exist in a subshell by dividing the number of groups in a block by #2#

#"no. of orbitals in a subshell" = "no. of groups in the block"/2#

This is the case because an orbital can hold a maximum of #2# electrons as stated by the Pauli Exclusion Principle.

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