# Consider the following sets of quantum numbers. Circle all of the allowed sets of quantum numbers for an electron in a hydrogen atom. The electron may be either in a ground state or an excited state?

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a) n=2, l=1, ml =-1, ms=+1/2

b) n=2, l=1, ml =2, ms=+1/2

c) n=2, l=2, ml =1, ms=+1/2

d) n=3, l=0, ml =0, ms=-1/2

e) n=3, l=1, ml =0, ms=0

f) n=0, l=0, ml =0, ms=-1/2

a) n=2, l=1, ml =-1, ms=+1/2

b) n=2, l=1, ml =2, ms=+1/2

c) n=2, l=2, ml =1, ms=+1/2

d) n=3, l=0, ml =0, ms=-1/2

e) n=3, l=1, ml =0, ms=0

f) n=0, l=0, ml =0, ms=-1/2

##### 1 Answer

Here's what I got.

#### Explanation:

All you have to do here is compare the values given to your for the principal, angular momentum, magnetic, and spin quantum numbers with the **allowed values** they can take in relation to each other.

You will have

**(a)**#" "n=2, l=1, m_l = 1, m_s = +1/2" "color(green)(sqrt())#

This set is valid because all four quantum numbers have allowed values. The angular momentum quantum number can take values ranging from

#l=0" "# and#" "color(darkgreen)(ul(color(black)(l=1)))#

The magnetic quantum number can take values ranging from

#m_l = {-1, color(white)(-)0, color(darkgreen)(ul(color(black)(+1)))}#

Finally, the spin quantum number can take the value

**(b)**#" "n=2, l=1, m_l = 2, m_s = +1/2" "color(red)(xx)#

This set is **not** valid because the magnetic quantum number has a value that is not allowed for

**(c)**#" "n=2, l=2, m_l = +1, m_s = +1/2" "color(red)(xx)#

This set is **not** valid because the angular momentum quantum number cannot take the value

**(d)**#" "n=3, l=0, m_l = 0, m_s = -1/2" "color(green)(sqrt())#

This set is valid because all four quantum numbers have allowed values. The angular momentum quantum number can take the value

Likewise, the magnetic quantum number can take the value **only allowed value** for the magnetic quantum number when

**(e)**#" "n=3, l=1, m_l = 0, m_s = 0" "color(red)(xx)#

This set is **not** valid because the spin quantum number can only take two values,

**(f)**#" "n=0, l=0, m_l = 0, m_s = -1/2" "color(red)(xx)#

This set is **not** valid because the principal quantum number cannot take the value