Question

How many orbitals does the principle quantum number n=3 have? Please help I NEED an explanation

Answer 1

In an atom, no two electrons can have the same set of 4 quantum numbers - n, l, ml and ms. This rule is called the Pauli Exclusion Principle, and it is this set of numbers which helps define unique characteristics owing to each electron.

http://chemwiki.ucdavis.edu/Physical_Chemistry/Quantum_Mechanics/Quantum_Theory/Trapped_Particles/Atoms/Quantum_Numbers

This link should provide you with a bit more detail into what each of the quantum numbers stand for. It can get rather complicated and confusing, but the main point of it is that if we know the principal quantum number, n, or the energy level, then we can work out the possible set of 4 quantum numbers (n, l, ml, ms) for any electron at this level.

So,
- n (principal quantum number) defines the distance the energy level/shell is away form the nucleus. It can be any individual number from n=1,2,3,4,......

- l (orbital angular momentum number) defines the shapes of the possible subshells at this energy level n. These subshells are regions in which we could possibly find an electron at this energy level, and you may be familiar with the names of some of them such as s, p, d and so on. When working out the number of subshells present, we give each of them a numeric value (0 = s, 1 = p, 2 = d, 3 = f, and so on from the lowest energy subshell, s, up to the highest). We then say for a given shell at n, the subshells present there will be 0,1,...,n-1. SOMETIMES YOU'LL SEE THESE s,p,d,... SUBSHELLS ALSO REFERRED TO AS 'ORBITALS', BUT I'LL CONTINUE TO CALL THEM SUBSHELLS FOR CLARITY.

-ml (magnetic quantum number) DEFINES THE NUMBER OF SPECIFIC ORBITALS WITHIN EACH OF THE AVAILABLE SUBSHELLS (AND THEIR ORIENTATION) AT A GIVEN ENERGY LEVEL, n. At any energy level/principal quantum number, an available subshell will contain a characteristic number of specific orbitals (or parts) for that subshell, with each orbital able to hold two electrons. So, given an available subshell with a angular momentum number l, the orbitals in this shell are represented by -l,..,0,...l.

-ms (spin quantum number) defines the spin a certain electron has if it is located in one of these orbitals, in a certain subshell, at a certain energy level. It will either be +1/2 or -1/2, as no two electrons in the same orbital can have the same spin, as that would mean that they would have identical sets of 4 quantum mechanical numbers.

Answer 2

Confused yet? Don't worry - they're just the main rules....things should become a lot clearer when we look at the question you asked. Again, when you ask how many orbitals are available at n=3, then I'll assume you're on about the specific orbitals (ml) within a given subshell, and not the subshells themselves.

-So, first of all, we know that our principal quantum number, n, is equal to three (n = 3).

-Now, we can go about working out the possible subshells at n = 3, though the orbital angular momentum number, l. Remembering the rule we said above:

l = 0,1,2,...,n-1

So, this means that for n = 3, we would have subshells at l=0, l=1 and l=2 (i.e. we would have subshells for l starting at zero and working our way up to l = n-1, which in this case is l = 2)

- Lets now treat each of these subshells separately to work out how many orbitals are in each, remembering our rule from above in relation to the magnetic quantum number, ml.

ml = -l,...,0,....+l

- The subshell l = 0 (or the s-subshell) will hence have orbitals represented by ml = -0,...0,...,+0. This makes no sense of course with -0 and +0, and as there are no whole numbers between 0 and 0, we just say that there is ONE orbital, represented by ml = 0.

- The subshell l = 1 is next (or the p-subshell). Following the same rules as before, this will have orbitals represented by the whole numbers ml = -1,...0,...,+1. Again there are no whole numbers between -1 and 0 and 0 and +1, so we can simplify this to
ml = -1,0,+1.
These are our three orbitals for this subshell, as represented by the THREE numbers above ml = -1, ml = 0 and ml = +1.

-Finally, we'll look at the subshell l = 2 (or the d-subshell). As before, this subshell will contain orbitals represented by the whole numbers -2,...,0,...+2. We know that there are whole numbers between -2 and 0 and 0 and +2, so we can rewrite this range as:
ml = -2,-1,0,+1,+2
These are our FIVE orbitals for this subshell, as represented by the numbers ml = -2, ml=-1, ml = 0, ml = +1 and ml = +2.

We don't need to worry about the final spin quantum number, as we are only interested in finding out about the orbitals, not the individual electrons which go into them. So, we can add up all the orbitals present in each available shell at n = 3 to give us:

1 + 3 + 5 = 9 orbitals overall.



Hope that helps you! :)

Answer 3

Thank You!!