Could someone explain the meaning of n,l,m and how they derive those ratios/numbers?

n. Takes values from 1 upwards.

You can sort of think of it like the rows on the periodic table. The first row elements fill up the n = 1 orbitals, the second row elements fill up the n = 2 orbitals. The transition metals are offset by 1 row (as in they're in the 4th row but they fill up the 3d orbitals). The f block is offset by 2 rows, they fill up the 4f and 5f orbitals when they're on the 6th and 7th rows.

l. Takes any value from 0 to n-1.

When n = 1 the only possible value for l is 0. This is why the first energy level only has an s orbital, the 1s orbital.

When n = 2 l can be either 0 or 1. This is why the second energy level has both an s orbital and p orbitals.

m. Takes values from -l to +l including 0.

When l = 0 (s orbital), m can only be equal to 0. This is why there is only ever one s orbital per energy level.

When l = 1 (p orbital), m can be equal to -1, 0 or +1. This is why there are three p orbitals per energy level (px, py, pz).

For any value of n there are n2 orbitals. If n = 1 there's only an s orbital (12 = 1). If n = 2 there is an s orbital and three p orbitals (22 = 4). If n = 3 there is an s orbital, three p orbitals and five d orbitals (32 = 9).

Orbitals in electron configurations are designated like this:

nlnumber of electrons

Hydrogen's electron configuration is 1s1. 1 electron in the 1s orbital. Helium's electron configuration is 1s2. 2 electrons in the 1s orbital.

Lithium's electron configuration is 1s2 2s1. 2 electrons in the 1s orbital, 1 electron in the 2s orbital.

A "closed shell" configuration (as in a noble gas configuration) will sometimes be used to save space.

Lithium's configuration could also be written as [He] 2s1 where [He] represents the electron configuration of helium atom (1s2).

Doesn't save much space there but it's much easier to see [Ar] 3d6 4s2 than 1s2 2s2 2p6 3s2 3p6 3d6 4s2 which is the electron configuration for iron.

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