Quantum Numbers?

Question

When writing quantom numbers for elements how do I know when "n" (The Principal Quantum Number) should go from 1 to 2 to 3 etc.. and how do I know what Ml (The Magnetic Quantum Number) should be depending on what and "l" are?

Also, how do I know how many electrons can occupy an orbital represented by something like n=2, l=1, ml=-1?

Answer 1

If you're giving the quantum numbers to identify an element, the quantum numbers usually refer to the quantum numbers of the outermost electron(s).

So say you're doing lithium (Li):

Li has an electronic configuration of 1s2 2s1

n is equal to the energy level of the outermost electron. Since the outermost electron is in the second energy level, n=2.

The quantum number "L" refers to the orbital.

s => L=0
p => L=1
d => L=2

So in the case of Li, L=0 since the outermost electron is in an s orbital.

ML tells you which of the slots of an orbital the outermost electron is in. Each "slot" can fit two electrons. The number of slots is consistent with the number of electrons which can be in an orbital. Also, ML always has values from -L to +L. So if L=0, ML is only equal to 0 (One slot labeled "0" for two electrons). If L had been 1 (a p orbital), ML would have been -1, 0, and 1. That's three slots for six electrons.

Answer 2

When doing quantum numbers you have to think of them like an address for electrons. The way I relate it to my students is like this:
"n" represents the energy level the electron is in. "n" is like the country you live in. The energy level can be separated into sublevels, just like the USA is separated into states.
"l" is the sublevel the electron is in, similar to the state you live in. Sublevels can be separated into orbitals, just like states can be separated into counties.
"m" represents the orbital the electron is in, similar to the county (or city) you live in.

The value of "n" depends on the number of energy levels the atom has. You can figure out the maximum number of energy levels an atom has by looking at what row it is in on the periodic table. Each energy level can hold a certain number of electrons. This is determined by "l" and "m". If n=1, then l=0 (l equals n-1). This 0 actually represents the s sublevel. That means the first energy level only has one sublevel (s). If n=2, then l=0 and 1, meaning the second energy level has two sublevels (s and p). This continues: the third energy level has three sublevels (s, p, and d), and energy levels four and above have four sublevels (s, p, d, and f).

Each sublevel has a specific number of orbitals (s has 1, p has 3, d has 5, and f has 7) and each orbital can hold two electrons. So, since the first energy level only had the s sublevel, it also only has 1 orbital and can hold 2 electrons. The second energy level has two sublevels, s (1 orbital) and p(3 orbitals), so can hold a total of 8 electrons. The third energy level can hold 18 electrons, and so on.

These orbitals are determined by "m", which equals -"l" to +"l". So if l = 0, m = 0, meaning 1 orbital. If l=1, m= -1, 0, +1 meaning three orbitals (which makes sense since l=1 means p which has three orbitals).

The example you gave where n=2, l=1, m=-1 is refering to the electrons in the second energy level, the second sublevel (which is p), and the first orbital (out of three). Since it is refering to the orbital, that means two electrons can occupy that orbital. ALL orbitals can only hold 2 electrons.

Quantum numbers can be very confusing, but I hope this has helped some!

Answer 3

the quantic number l may assume values from 0 to n-1

when n = 3 >> l = 0 , 1 , 2

the magnetic quantum number has values from - l to +l

when l = 0 >> m = 0 s orbital 2 electrons

l = 1 >> m = - 1 , 0 , + 1 p orbital 6 electrons

l = 2 >> m = - 2 , -1 , 0 , + 1, + 2 d orbital 10 electrons



n =2 >> l = 0 m = 0 2 electrons

n = 2 >> l = 1 m = -1 , 0 , +1 6 electrons

Answer 4

n will go as high as you need in order to accomodate the number of electrons for the given element.

As you know, there are three quantum numbers that specify a given orbital. For a given n, there are from 0 to n-1 L's in steps of one for that given n. There are from -L to L, m numbers in steps of 1. It's easiest to just do an example, so say we have a bunch of electrons to put around a nucleus.

We start with n=1:

because n=1, L=n-1=0, thus m=0. this means the ONLY orbital for n=1 is specified by (n,L,m)=(1,0,0)

TWO electrons can occupy any ONE orbital, thus we can fit two electrons in the above orbital. If we have more than 2 electrons, we move on to n=2:

For n=2, n-1=1, thus L can be 0 or 1. If L=0, then m=0. If we take L=1, well then, following the rules above, m can be -1,0, or 1. This means there are the following orbitals for n=2:

(2,0,0), (2,1,-1), (2,1,0), and (2,1,1)

this means we can accomodate 8 more electrons (2xthese four orbitals) before moving on to n=3, where again, we'll follow the same rules and find the following combos are possible:

(3,0,0) (3,1,-1) (3,1,0) (3,1,1) (3,2,-2) (3,2,-1) (3,2,0) (3,2,1) (3,2,2)

Here's the kicker: that in a multi-electron ATOM these last last 5 orbitals are higher in energy (filled after) the (4,0,0) orbital--just when you thought it was going to be easy! Look at a periodic table: The ROWS correspond to the number n, and you move left to right, filling in electrons. For n=1, we had the one orbital, it can fit up to two electrons, so there are two elements on the first row, H, and He. Moving to n=2, we found there were 4 orbitals, which can hold up to 8 electrons, so there are 8 elements on row 2. Row 3 is where problems arise, because we don't use all of the n=3 orbitals yet, only those with the lower L numbers, namely 0 and 1. We then fill the (4,0,0) orbital, row 4 with two electrons, getting us K and Ca. THEN we GO BACK and fill those previous five n=3 orbitals with up to two electrons giving us the ten elements Sc through Zn. Then we fill the three orbitals (4,1,-1), (4,1,0) and (4,1,1) with two electrons each to give us the rest of the six elements on row 4. You may wonder about all the possible other orbitals for n=4, but they don't start filling in until much later, (the actinide and lanthanide series at the bottom of the table). The object is to keep L low. For the record L=0 is called an s-orbital (from old spectrographic notation), L=1 is called p, and L=2 is called d, L=3 is called f. To remove all ambiguity, this is how you can stack electrons into orbitals (in the order of top to bottom, left to right):

(1,0,0) holds up to two electrons before moving on to n=2:

(2,0,0), (2,1,-1), (2,1,0), (2,1,1) hold up to eight electrons before moving on to:

(3,0,0), (3,1,-1), (3,1,0), (3,1,1) hold another eight before moving on to:

(4,0,0), (3,2,-2), (3,2,-1), (3,2,0), (3,2,1), (3,2,2) (4,1,-1) (4,1,0) (4,1,1) hold a whopping 18 electrons before moving on to n=5:

(5,0,0) (4,2,-2) (4,2,-1) (4,2,0) (4,2,1) (4,2,2) (5,1,-1) (5,1,0) (5,1,1)

At which point I'll stop and let you look at a periodic table, because after (6,0,0) you GO BACK to (4,3,x) which gives 7 orbitals and then (5,2,x) another five orbitals before finishing with the set of three (6,1,x) orbitals, which is (1+7+5+3)x2=32 elements on row 6, 15 of which are cut out and put at the bottom of the chart so you don't have to make a chart that is 32 elements wide!

Answer 5

A quantum selection describes the energies of electrons in atoms. each and each quantum selection specifies the fee of a conserved volume in the dynamics of the quantum gadget. it particularly is any of a collection of authentic numbers assigned to a actual gadget that throughout the time of my view signify the residences and together specify the state of a particle or of the gadget.