# Electron Orbitals Cartoon courtesy of lab-initio.com.

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Electron Orbitals Cartoon courtesy of lab-initio.com

The Bohr Model of the Atom
I pictured electrons orbiting the nucleus much like planets orbiting the sun. But I was wrong! They’re more like bees around a hive. Neils Bohr

Quantum Mechanical Model of the Atom
Mathematical laws can identify the regions outside of the nucleus where electrons are most likely to be found. These laws are beyond the scope of this class…

Heisenberg Uncertainty Principle
“One cannot simultaneously determine both the position and momentum of an electron.” You can find out where the electron is, but not where it is going. OR… You can find out where the electron is going, but not where it is! Werner Heisenberg

Modern Quantum Theory As a direct result of Schrondinger’s equation, the first 3 quantum numbers were derived to show properties of –e in specific orbitals in which they are located in These equations paved the way for quantum theory describing mathematically wave properties of the –e and other small particles

First 3 Quantum Numbers describe
1- main energy level 2-shape of orbital 3- orientation of orbital 4th quantum number describes state of –e occupying the orbital (spin number)

#1- Principle QN-n (main energy level)
Total number of orbitals existing in a shell (energy level) =n2 All main energy levels has sublevels (suborbitals) of different shapes Value-positive only- 1, 2, 3… 7 -e whose n=1 occupies lowest energy level (closest to the nucleus)

Electron Energy Level (Shell)
Generally symbolized by n, it denotes the probable distance of the electron from the nucleus. “n” is also known as the Principle Quantum number Number of electrons that can fit in a shell: 2n2

Electron Orbitals An orbital is a region within an energy level where there is a probability of finding an electron. Orbital shapes are defined as the surface that contains 90% of the total electron probability.

#2- Angular Momentum-l (shape of orbital)
Also known as azimuthal QN For specific energy level, the number of sublevels possible =n Value of 0 and all positive integers less than or equal to n-1 Examples: n=2, 2 shapes l=0 represents s l=1 represents p

f- too complicated to discuss
More about shapes s orbital- n=1- sphere p orbital- n=2- dumbell d- complex f- too complicated to discuss

s Orbital shape The s orbital has a spherical shape centered around
the origin of the three axes in space.

p orbital shape There are three dumbbell-shaped p orbitals in each energy level above n = 1, each assigned to its own axis (x, y and z) in space.

More QN and shapes 1st energy level, n=1- only s orbital
2nd energy level, n=2- only s and p 3rd energy level, n=3- s, p and d 4th energy level, n=4- s,p,d and f

d orbital shapes Things get a bit more complicated with the five d orbitals that are found in the d sublevels beginning with n = 3. To remember the shapes, think of “double dumbells” …and a “dumbell with a donut”!

Shape of f orbitals

1 s orbital-spherical only-
#3- Magnetic QN-m 1 s orbital-spherical only- 1 orientation (m=0) 3 p orbitals-3 orientations x,y,z (m= -1, m= 0, m= 1) and so on for d and f

more 5 d orbitals- orientation has values of
m= -2, m= -1, m= 0, m= 1, m=2 representing dx2-y3,dxy, dzy, dxz, dz2 7 f orbitals-number of orbitals in each energy level equals n2 If n=1, n2=1 or if n=3 then n2=9, etc

#4- Spin QN Value +1/2 or –1/2 Indicates fundamental spin state of the –e (-e spin on axis in one of two directions or states) Spin creates a magnetic field and accounts for the magnetic properties of –e (remember cathode ray and magnet)

WRITING QN Each orbital show by its principle QN followed by letter of suborbital 1s or 3p or 4d

Orbital filling table

Electron configuration of the elements of the first three series