What are the possible values of quantum number ℓ when n =1 ?

1 Answer
Mar 22, 2018

Answer:

#l=0#

Explanation:

The relationship between the possible values of the angular momentum quantum number, #l#, and the principal quantum number, #n#, is given by

#color(blue)(ul(color(black)(l = {0, 1, 2, ..., n-1})))#

For a given quantum number #n#, the angular momentum quantum number can take #n# possible values that range from #0# to #n-1#.

In your case, you have #n=1#, which means that the angular momentum quantum number can take #1# possible value.

#l = 0#

This tells you that the first energy shell can hold a single energy subshell, the #s# subshell.

#n = 1, l= 0#

The electron is located in the first energy shell, in the #1s# subshell.

Consequently, the first energy shell can hold a single orbital, the #1s# orbital, because the magnetic quantum number, #m_l#, which tells you the number of distinct orbitals present in a given subshell, can take one possible value.

#m_l = {-1, - (l-1), ..., -1, 0, 1, ..., l-1, l}#

So for #l=0#, you have

#m_l = 0 -># the #s# orbital

And so

#n =1, l= 0, m_l = 0#

The electron is located in the first energy level, in the #1s# subshell, and in the #1s# orbital.