Atomic Orbitals & Quantum Numbers

Quantum Numbers

There are 4 Quantum numbers needed to describe the orientation of an election

Principal Energy Level = n (1, 2, 3, 4…7)

Sublevel or angular momentum quantum level (s, p, d, f)

Orbital or magnetic quantum level

Spin (two possible directions of spin)

Quantum Numbers

The main energy level of electrons is given by the Principal Quantum Number (n)

“n” must equal integers 1,2,3,4,etc.

1st energy level, n=12nd energy level, n=23rd energy level, n=3

• Within each energy level, there are several possible cloud shapes that are energy sublevels.

These sublevels are calculated from the angular momentum quantum number “l”. l values are usually given with the letters s, p, d, f.

Orbitals

• Orbitals• s orbitals are spherical spherical • p orbitals are dumbelldumbell shaped • d orbitals are cloverleafcloverleaf shaped except for 1 • f orbitals have a variety of strange shapes

• Remember these shapes correspond to the probability of finding an electron in each area.

“s” Orbitals

“p” Orbitals

“d” Orbitals

“f” Orbitals

More on Quantum Numbers

• The magnetic quantum number “m” gives the orientationorientation of the atomic orbital on the x, y, or z axis.

• The spin quantum number is either +1/2 or –1/2 indicating clockwise or counterclockwisecounterclockwise spin.

More On OrbitalsPrincipal Energy Level Possible sublevels

n=1n=1 ss

n=2n=2 s,ps,p

n=3n=3 s,p,ds,p,d

n=4n=4 s,p,d,fs,p,d,f

n=5n=5 s,p,d,fs,p,d,f

n=6n=6 s,p,d,fs,p,d,f

n=7n=7 s,p,d,fs,p,d,f

Orbitals & SublevelsType of Orbital

# orbitals in it Total electrons in sublevel

ss 11 22

pp 33 66

dd 55 1010

ff 77 1414

Questions1) How many electrons are in the 2nd principal

energy level (n=2)?

2) How many orbitals are in the 4th principal energy level (n=4)?

3) How many sublevels in the 3rd principal energy level (n=3)?

8 electrons2 in the 2s sublevel and 6 in the 2p sublevel

16 orbitals4th energy level has s, p, d, and f sublevelss = 1 orbital, p = 3 orbitals, d = 5 orbitals, f = 7 orbitals

3 sublevels3s, 3p, 3d

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1,120,000!