Lecture 20 Chapter 7 Sections 4-6

• Transitions – spectroscopy

• de Broglie

• Heisenberg

• Quantum Numbers

• Orbitals

Announcements

• Two seminars Today– Bio – bioinformatics SC1019 3:00– Chemistry SC1000 4:00

• Advising session for freshman (FREE!)– 6:15 Wednesday, 26 October, VDW102

• Exam 2 is two weeks from today– Do lots of book problems– READ CHAPTER 7

Early Quantum Mechanics

• Many huge discoveries at turn of century– Photoelectric effect just one of them

• Led to understanding that electrons in atoms have only certain specific energies they can exist at.

• For H, the electron can have the following potential energies:

• Note energies are negative – electron is bound• These quantized energies lead to an energy level diagram

2

181018.2 n

JEn

−×−= where n = 1,2,3…

Which sketch corresponds to the possible energies of an electron in a hydrogen atom?

54321

25%25%25%25% 1.

2.3.4.

Quantized Energies

• Energy can by gained or lost in only specific amounts – quanta

• Ground state: lowest energy state of an atom.

• Excited state: higher energy states – reached by absorbing light (usually)

• Energy level diagram: depicts the changes in energy of an atom

• When an atom emits a photon (or heat), it returns to a lower state.

• ∆E=± hυphoton

ABSORPTION

EMISSION

n1

n1s 10 3.29υ 2

22

1

115

−×= −

For Hydrogen (Balmer)

n1

n1s 10 3.29υ 2

22

1

115

−×= −

de Broglie

• Recall light has both wave and particle properties• de Broglie said that all things have both wave and particle

properties.

muh

particle =λ

• Where m is mass and u is velocity • Wave properties of matter most easily observed for

things with small mass (big wavelength)

See also Figure 7-15 (p.277)

1. A particle occupies a particular location, but a wave has no exact position.

2. Because of their wave-like properties, electrons are always spread out in space.

3. As a result, the position of an electron cannot be precisely defined.4. Therefore, electrons are delocalized, rather than pinpointed.

The Heisenberg Uncertainty Principle says that the more accurately we know position, the more uncertain we are about energy, and vice versa.

Since we know electron energies very well (quantum mechanics) we can’t know their positions precisely.

So instead, we identify “probable locations” of the electrons in an atom, not a exact locations – these are orbitals

Heisenberg

Quantum Numbers

• The n in the H-atom energy equation is an example of a quantum number

• Simply a way of accounting for all of the possible states – all of the possible ways that electrons can behave

• We will have several different quantum numbers – they all work together to describe the possible quantum states– n– l– ml

– ms

2

181018.2 n

JEn

−×−=

Principal Quantum Number

• n = 1, 2, 3…to infinity (positive integers)• Describes the energy of the electron and the average distance from the

nucleus.• As n increases, so does the energy of the electron, and the average

distance from the nucleus.• Corresponds to an electron shell• Therefore, if two different electrons have n=1 for an atom, then they

are in the same shell.

Azimuthal Quantum Number

• l = 0, 1, 2, 3, …, n-1• So, if n = 1, then there is only one option for l• If n = 3, then l can have three values, 0, 1, and 2• the value of l corresponds to an orbital shape and we assign letters to

describe the shapeValue of l Subshell Label

0 s1 p2 d3 f

Magnetic Quantum Number

• Orbitals described by l can have direction– A football is similar to an l = 1 orbital

• Therefore, orbitals must have their orientation described• ml = 0, ±1, ±2, ±3,…±l• So, if l = 1, then ml can be -1, 0, or 1

Spin Orientation Quantum Number

• An electron also has magnetism associated with a property called spin. – The electron is not literally spinning by the way

• Just as magnetism is directional, so is spin.• Electron spins have two orientations• Possible values: ms = + ½ (up) and – ½ (down)

Table 7 – 2 Restrictions on Quantum Numbers on Atoms

Orbital shapes

• n describes the orbital’s size (and a little bit about shape)• l is the primary shape descriptor• ml describes the orientation• ms is not related to orbital shape

• Nice webpage to supplement pictures in text:www.shef.ac.uk/chemistry/orbitron/index.html

• We’ll talk about how electrons fit into orbitals next week.

Today• Go to seminar

By Monday• Read Chapt 7 carefully• Work extra problems!• Start CAPA #12

Remember: You are done with the homework when you understand it!