In an atom, what is the maximum number of electrons that can have the following quantum numbers?

Question

In an atom, what is the maximum number of electrons that can have the following quantum numbers?

(D) n=7, I=5, m1= +2

Answer 1

Quantum numbers

n is the principal q.n. and starts at 1 ...

l is the azimuthal q.n. and starts at n minus 1 so 0 ...

ml is the magnetic q.n. and ranges from -l to +l

ms is the spin q.n. and can be either -1/2 or +1/2

So, let's start with n = 1

then l can only be 0

and ml can only be 0

but ms can still be either -1/2 or +1/2

Thus, one electron will have the set of q.n.

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

This is an electron in the 1s orbital with negative spin

And another electron will have the set of q.n.

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

This is the other electron in the 1s orbital with positive spin

Notice that the "1" comes from n, the principal q.n.

and that the s orbital comes from l, the azimuthal q.n.

The opposite spinning electrons can pair

I assume you know that with n = 2, we'll get one 2s and three 2p orbitals

For the electrons in 2s, similar to those in 1s

n = 2, l = 0, ml = 0 and the two ms at -1/2 and +1/2

Since l can go to n-1,

we'll see a set of q.n. with l = 1 and ml ranges from -l to +1

Let's look at them:

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

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

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

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

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

n = 2, l = 1, m1 = +1, ms = +1/2

These six sets of quantum numbers are assigned to each of the six 2p electrons.

Now, let's put into play the set of q.n. you've been give

n = 7

l = 5

m1 = +2

since nothing was said about ms, we're going to assume both ms = -1/2 and ms = +1/2 will be considered

If l = 1 is a p orbital, what is the type of orbital when

l = 2? You should be able to come up with d orbital for this

l = 3? You should be able to come up with f orbital for this

l = 4? Not sure most students know that g orbital comes after

l = 5? And h orbital for this one

With l = 5, ml can range from -5 to +5

-5, -4, -3, -2, -1, 0 +1, +2, +3, +4, +5 but you are only asked to consider

ml = +2

n = 7, l = 5, ml = +2, ms = -1/2

n = 7, l = 5, ml = +2, ms = +1/2

Notice that whenever the first three types of q.n. are specified,

you are dealing with a very specific orbital

and any orbital can only contain two electrons negatively and positively spinning in order not to repel each other.

I hope this explains a not so easy concept in chemistry that looks like it has moving points and cannot be pinned down. I usually don't provide an answer to questions/problems but just offer guidance but this one naturally comes to a conclusive answer ... esp if n = 7, l = 5, and ml = +2 ...