# Circle all of the allowed sets of quantum numbers for an electron in a hydrogen atom?

##
n=6, l=3, ml =-2, ms=+1/2

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

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

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

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

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

n=6, l=3, ml =-2, ms=+1/2

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

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

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

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

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

##### 1 Answer

**Recall the quantum numbers:**

The three main **quantum numbers** describe the **energy level**, **shape**, and **projection** of the orbitals onto the xyz axes. Bonus: there is a fourth which describes the spin of the electron(s) in the orbital.

#n# is the**principle quantum number**which describes the energy level.#n >= 1# and is in the set of integers. That is,#n = 1,2, . . . , N# , for some finite#N# (only one of those numbers at a time).#l# is the**orbital angular momentum quantum number**which describes the shape of the orbital.#l >= 0# and is an integer.#l = 0, 1, 2, ..., n-1# for#s, p, d, ...# orbitals, respectively (only one of those numbers at a time).#m# (more specifically,#m_l# ) is the**magnetic quantum number**, which describes the projection of the orbital in the#0,pm1, pm2, . . . , pml# directions.

It takes on

everypossible value of#l# and#0# in integer steps (not justthevalue of#l# , but every integer from#-l# to#0# to#+l# ).That is,

#m_l = {0,pm1,pm2, . . . , pml}# . Note that#m_l# tells you how manysubshellsthere are for a given orbital type (#s,p,d, . . .# ).

#m_s# (see why we need to say#m_l# ?) is the**electron spin quantum number**, which describes the**spin**of the electron. It is only#pm1/2# , independent of the other quantum numbers.

**(1)**

With

For

This is really saying that there is a spin-up electron in the

#6f# orbital with an orbital angular momentum of#-2# (the second orbital from the left, for a#-3,-2,-1,0,+1,+2,+3# order).

**(2)**

With

For

This is really saying that there is a spin-down electron in the

#2p# orbital with an orbital angular momentum of#0# (the middle orbital for a#-1,0,+1# order).

**(3)**

With

For

For

Thus, this is an impossible configuration.

**(4)**

With

For **impossible**.

Thus, this is an impossible configuration.

**(5)**

With

For **forbidden**.

Thus, this is an impossible configuration.

**(6)**

With

Thus, this is an impossible orbital.