Electrons as waves

• Scientists accepted the fact that light has a dual wave- particle nature.

• De Broglie pointed out that in many ways the behavior of the Bohr’s quantized electron orbits was similar to the known behavior of waves.

• Electrons should be thought of as having a dual wave-particle nature also.

Evidence; Electrons

• Electron beams could be diffracted or bent.

• Electron beams demonstrated the properties of interference.

Heisenberg Uncertainty Principle

• Werner Heisenberg (1927)

• It is impossible to determine simultaneously both the position, and velocity, of an electron or any other particle.

Heisenberg explained

• To locate an object you would have to be able to look at it.

• When we see an object we actually are seeing the light waves that the object reflects.

• For us to see an object a photon of light has to hit it.

Heisenberg explained

• A photon hitting a book or an airplane has no noticeable affect.

• However, an electron is so small that once a photon its it, the electron undergoes a large energy change and is moved.

• Similarly, the collision between the photon and the electron causes the electrons velocity to change.

In summary

• If we were able to measure the location, the velocity would change

• If we were to measure the velocity, the location will change.

• Note: Treats electron like a particle

Schrodinger ‘s wave equation

• Developed an equation that treats electrons as waves. ( related the amplitude of the electron wave to any point in space around the nucleus).

Quantum theory

• Heisenberg’s uncertainty principle and Schrodinger’s equation laid the foundation for quantum theory.

• Quantum theory- describes mathematically the wave properties of electrons and other very small particles.

Probability

• Ceiling fan- where are the blades at any one moment?

Orbital

• Three dimensional region around the nucleus that indicates the probable location of an electron.

• These three dimensional shapes are named s, p, d, and f.

• When describing the location of the electrons in an orbital we are indicating that there is a 99 % chance that the electron will be found there.

Quantum numbers

• A list of three numbers that describe the location of the electron

• The numbers represent– The main energy level– The shape – The orientation of the orbital, axis

Spin of electron

• A fourth number indicates the spin within the orbital.

Principle quantum number

• 1-7 representing the energy level

• Symbolized by the letter n

• As n increases the distance from the nucleus increases

• As n increases the potential energy of the electron increases.

Angular momentum or orbitals

• The different shaped orbitals are also called sublevels.

• Symbolized by l, indicates the shape of the orbital

• 2 electrons are allowed in one orbital

• The number of orbital shapes, l, possible is equal to n ( up to n=4)

continued

• The values of l allowed are 0 and all possible integers up to n-1

• l= n-1 0 = s shape 1 = p shape 2 = d shape 3 = f shape

2 electrons per orbital

• The s shape has 1 orbital – total of 2 electrons• The p shape has 3 orbitals – 6 electrons• The d shape has 5 orbitals – 10 electrons• The f shape has 7 orbitals – 14 electrons

• See page 103• Each orbital is on a different axis, ( x,y,z etc. )

Magnetic quantum number

• Indicates the orientation of the orbital around the nucleus.

• Symbolized by the letter m

• Indicated by numbers on either side of zero

• The s shape has an m value of 0 ( no axis)

• The p shape has m values of –1,0,+1

• The d shape has m values of –2,-1,0,+1,+2

Summary

• n,l,m

• Energy level, shape, axis

SpinThe last number is a spin indicator

• -1/2 or + ½• These are the two spin states, ( spin to the right or

spin to the left)• No two electrons can be identical., or , no two

electrons can have the same set of quantum numbers – Pauli’s exclusion principle

• A maximum of two electrons can occupy an orbital, each will have a different spin.

Mathematical equations

• The number of orbitals per energy level is n2

n=2, there are 4 orbitals; 1 s and 3 pn=3 there are 9 orbitals; 1s, 3p, 5d

Number of electrons

• Since there are 2 electrons per orbital

• 2n2 is the number of electrons per energy level.