Section 4.2 “The Quantum Model of the Atom” Pre-AP Chemistry

Chapter 4 Vocabulary 12. Heisenberg uncertainty principle 13. Quantum theory 14. Orbital 15. Quantum number 16. Principal quantum number 17. Angular momentum quantum number 18. Magnetic quantum number 19. Spin quantum number

Chapter 4 Notes E. Quantum Model F. Quantum Numbers G. Atomic Orbitals H. Energy Levels

Chapter 4 Preview Lesson Starter Objectives Electrons as Waves Section 2 The Quantum Model of the Atom Chapter 4 Preview Lesson Starter Objectives Electrons as Waves The Heisenberg Uncertainty Principle The Schrödinger Wave Equation Atomic Orbitals and Quantum Numbers

Chapter 4 Lesson Starter Section 2 The Quantum Model of the Atom Chapter 4 Lesson Starter Write down your address using the format of street name, house/apartment number, and ZIP Code. These items describe the location of your residence. How many students have the same ZIP Code? How many live on the same street? How many have the same house number?

Lesson Starter, continued Section 2 The Quantum Model of the Atom Chapter 4 Lesson Starter, continued In the same way that no two houses have the same address, no two electrons in an atom have the same set of four quantum numbers. In this section, you will learn how to use the quantum-number code to describe the properties of electrons in atoms.

Section 2 The Quantum Model of the Atom Chapter 4 Objectives Discuss Louis de Broglie’s role in the development of the quantum model of the atom. Compare and contrast the Bohr model and the quantum model of the atom. Explain how the Heisenberg uncertainty principle and the Schrödinger wave equation led to the idea of atomic orbitals.

Chapter 4 Objectives, continued Section 2 The Quantum Model of the Atom Chapter 4 Objectives, continued List the four quantum numbers and describe their significance. Relate the number of sublevels corresponding to each of an atom’s main energy levels, the number of orbitals per sublevel, and the number of orbitals per main energy level.

Section 4.2 Quantum Model OBJECTIVES: Discuss Louis de Broglie’s role in the development of the quantum model of the atom

Section 4.2 Quantum Model OBJECTIVES: Compare and contrast the Bohr model and the quantum model of the atom.

Wave-Particle Duality J.J. Thomson won the Nobel prize for describing the electron as a particle. His son, George Thomson won the Nobel prize for describing the wave-like nature of the electron. The electron is a particle! The electron is an energy wave!

Ernest Rutherford’s Model Discovered dense positive piece at the center of the atom- “nucleus” Electrons would surround and move around it, like planets around the sun Atom is mostly empty space It did not explain the chemical properties of the elements – a better description of the electron behavior was needed

The Bohr Model of the Atom I pictured the electrons orbiting the nucleus much like planets orbiting the sun. However, electrons are found in specific circular paths around the nucleus, and can jump from one level to another. Niels Bohr

Confused? You’ve Got Company! “No familiar conceptions can be woven around the electron; something unknown is doing we don’t know what.” Physicist Sir Arthur Eddington The Nature of the Physical World 1934

Louis de Broglie “Given that light behaves as waves and particles, can particles of matter behave as waves?” He referred to the wavelike behavior of particles as matter waves. His reasoning led him to a mathematical expression for the wavelength of a moving particle

What is light?  = h/mv (from Louis de Broglie) Light is a particle - it comes in chunks. Light is a wave - we can measure its wavelength and it behaves as a wave If we combine E=mc2 , c=, E = 1/2 mv2 and E = h, then we can get:  = h/mv (from Louis de Broglie) called de Broglie’s equation Calculates the wavelength of a particle.

Chapter 4 Electrons as Waves Section 2 The Quantum Model of the Atom Chapter 4 Electrons as Waves French scientist Louis de Broglie suggested that electrons be considered waves confined to the space around an atomic nucleus. It followed that the electron waves could exist only at specific frequencies. According to the relationship E = hν, these frequencies corresponded to specific energies—the quantized energies of Bohr’s orbits.

Electrons as Waves, continued Section 2 The Quantum Model of the Atom Chapter 4 Electrons as Waves, continued Electrons, like light waves, can be bent, or diffracted. Diffraction refers to the bending of a wave as it passes by the edge of an object or through a small opening. Electron beams, like waves, can interfere with each other. Interference occurs when waves overlap.

The Heisenberg Uncertainty Principle Section 2 The Quantum Model of the Atom Chapter 4 The Heisenberg Uncertainty Principle German physicist Werner Heisenberg proposed that any attempt to locate a specific electron with a photon knocks the electron off its course. The Heisenberg uncertainty principle states that it is impossible to determine simultaneously both the position and velocity of an electron or any other particle.

The Schrödinger Wave Equation Section 2 The Quantum Model of the Atom Chapter 4 The Schrödinger Wave Equation In 1926, Austrian physicist Erwin Schrödinger developed an equation that treated electrons in atoms as waves. Together with the Heisenberg uncertainty principle, the Schrödinger wave equation laid the foundation for modern quantum theory. Quantum theory describes mathematically the wave properties of electrons and other very small particles.

The Schrödinger Wave Equation, continued Section 2 The Quantum Model of the Atom Chapter 4 The Schrödinger Wave Equation, continued Electrons do not travel around the nucleus in neat orbits, as Bohr had postulated. Instead, they exist in certain regions called orbitals. An orbital is a three-dimensional region around the nucleus that indicates the probable location of an electron.

Chapter 4 Electron Cloud Section 2 The Quantum Model of the Atom Click below to watch the Visual Concept. Visual Concept

Section 4.2 Quantum Model OBJECTIVES: Explain how the Heisenberg uncertainty principle and the Schrödinger wave equation led to the idea of atomic orbitals.

The physics of the very small Quantum mechanics explains how very small particles behave Quantum mechanics is an explanation for subatomic particles and atoms as waves Classical mechanics describes the motions of bodies much larger than atoms

Heisenberg Uncertainty Principle It is impossible to know exactly the location and velocity of a particle. The better we know one, the less we know the other. Measuring changes the properties. True in quantum mechanics, but not classical mechanics

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

It is more obvious with the very small objects To measure where a electron is, we use light. But the light energy moves the electron And hitting the electron changes the frequency of the light.

After Before Photon wavelength changes Photon Moving Electron Electron velocity changes

The Quantum Model Energy is “quantized” - It comes in chunks. A quantum is the amount of energy needed to move from one energy level to another. Since the energy of an atom is never “in between” there must be a quantum leap in energy. In 1926, Erwin Schrodinger derived an equation that described the energy and position of the electrons in an atom

Schrodinger’s Wave Equation Equation for the probability of a single electron being found along a single axis (x-axis) Erwin Schrodinger Erwin Schrodinger Quantum Leap TV intro

The Quantum Model Things that are very small behave differently from things big enough to see. The quantum mechanical model is a mathematical solution It is not like anything you can see (like plum pudding!)

The Quantum Model Has energy levels for electrons. Orbits are not circular. It can only tell us the probability of finding an electron a certain distance from the nucleus.

The Quantum Mechanical Model e- found inside blurry “electron cloud” (area where there’s chance of finding e-) fan blades bicycle wheel

The Quantum Model The atom is found inside a blurry “electron cloud”

Chapter 4 Notes E. Quantum Model 1. Louis de Broglie e- exists as waves at specific frequencies can be bent (diffraction) and interfere with each other (interference) 2. Werner Heisenberg -Heisenberg Uncertainty Principle - impossible to determine simultaneously both positon and velocity of an e-

Chapter 4 Notes E. Quantum Model 1. Louis de Broglie 2. Werner Heisenberg (Uncertainty Principle) 3. Erwin Schrödinger Wave Equation developed equation to treat e- as waves responsible for 3 of the 4 quantum numbers

Section 4.2 Quantum Model OBJECTIVES: List the four quantum numbers and describe their significance.

Section 4.2 Quantum Model OBJECTIVES: Relate the number of sublevels corresponding to each of an atom’s main energy levels, the number of orbitals per sublevel, and the number of orbitals per main energy level.

Atomic Orbitals and Quantum Numbers Section 2 The Quantum Model of the Atom Chapter 4 Atomic Orbitals and Quantum Numbers Quantum numbers specify the properties of atomic orbitals and the properties of electrons in orbitals. The principal quantum number, symbolized by n, indicates the main energy level occupied by the electron. The angular momentum quantum number, symbolized by l, indicates the shape of the orbital.

Atomic Orbitals and Quantum Numbers, continued Section 2 The Quantum Model of the Atom Chapter 4 Atomic Orbitals and Quantum Numbers, continued The magnetic quantum number, symbolized by m, indicates the orientation of an orbital around the nucleus. The spin quantum number has only two possible values—(+1/2 , −1/2)—which indicate the two fundamental spin states of an electron in an orbital.

Quantum Numbers and Orbitals Section 2 The Quantum Model of the Atom Chapter 4 Quantum Numbers and Orbitals Click below to watch the Visual Concept. Visual Concept

Shapes of s, p, and d Orbitals Section 2 The Quantum Model of the Atom Chapter 4 Shapes of s, p, and d Orbitals

Electrons Accommodated in Energy Levels and Sublevels Section 2 The Quantum Model of the Atom Chapter 4 Electrons Accommodated in Energy Levels and Sublevels

Electrons Accommodated in Energy Levels and Sublevels Section 2 The Quantum Model of the Atom Chapter 4 Electrons Accommodated in Energy Levels and Sublevels

Quantum Numbers of the First 30 Atomic Orbitals Section 2 The Quantum Model of the Atom Chapter 4 Quantum Numbers of the First 30 Atomic Orbitals

Chapter 4 Notes F. 4 Quantum Numbers Principal Quantum Number (n)- energy level - distance from nucleus: levels 1-7 2. Angular Momentum Quantum Number (l= 0,1,2,3) – shape: s,p,d, or f 3. Magnetic Quantum Number (m) – orientation - x, y, or z axis 4. Spin Quantum Number (- ½, + ½) - spin - 2 e- with opposite spin in same orbital * First 3 Quantum numbers came from Schrödinger's equation

Chapter 4 Notes G. Atomic Orbital Shapes 1. s = = 2. p = = 3. d = (4/5) = 4. f = = spherical 1 orbital = 2 e- (s2) dumbbell 3 orbitals = 6 e- (p6) cloverleaf 5 orbitals = 10 e- (d10) complicated 7 orbitals = 14 e- (f14)

Orbital Location on Periodic Table

Atomic Orbitals Principal Quantum Number (n) = the energy level of the electron: 1, 2, 3, etc. Within each energy level, the complex math of Schrodinger’s equation describes several shapes. These are called atomic orbitals (coined by scientists in 1932) - regions where there is a high probability of finding an electron. Sublevels- like theater seats arranged in sections: letters s, p, d, and f

Principal Quantum Number Generally symbolized by “n”, it denotes the shell (energy level) in which the electron is located. Maximum number of electrons that can fit in an energy level is: 2n2 How many e- in level 2? 3?

Notecard: Max e- in principle energy level (n) Maximum number of electrons that can fit in an energy level is: 2n2

Summary 2 6 10 14 # of shapes (orbitals) Maximum electrons Starts at energy level 2 s 1 1 6 p 3 2 10 d 5 3 7 14 4 f

By Energy Level First Energy Level Second Energy Level Has only s orbital 1s2 (1 orbital) 2 electrons Second Energy Level Has s and p orbitals available 2 in s, 6 in p 2s22p6 (4 orbitals) 8 total electrons s and p orbitals 1:20

By Energy Level Third energy level Has s, p, and d orbitals 2 in s, 6 in p, and 10 in d 3s23p63d10 18 total electrons Fourth energy level Has s, p, d, and f orbitals 2 in s, 6 in p, 10 in d, and 14 in f 4s24p64d104f14 32 total electrons d orbitals 3:40

By Energy Level Any more than the fourth and not all the orbitals will fill up. You simply run out of electrons The orbitals do not fill up in a neat order. The energy levels overlap Lowest energy fill first.

Chapter 4 Notes H. Energy Levels 1 = 1 sublevel = 1s = 2 = 2 sublevels = 2s, 2p = 3 = 3 sublevels = 3s, 3p, 3d = 4 = 4 sublevels = 4s, 4p, 4d, 4f = 2e- 8 e- 18 e- 32 e-

Summary of Principal Energy Levels, Sublevels, and Orbitals Number of sublevels Type of sublevel Max # of electrons Electron configuration n = 1 1 1s (1 orbital) 2 1s2 n = 2 2s (1 orbital 2p (3 orbitals) 8 2s2 2p6 n = 3 3 3s (1 orbital) 3p (3 orbitals) 3d (5 orbitals) 18 3s2 3p6 3d10 n = 4 4 4s (1 orbital) 4p (3 orbitals) 4d (5 orbitals) 4f (7 orbitals) 32 4s2 4p6 4d10 4f14

Sec 4.2 Practice Problems 1. How many sublevels are in the following principal energy levels? List the sublevels. a. n = 1 b. n = 2 c. n = 3 d. n = 4 1 1s2 2 2s2 2p6 3s2 3p6 3d10 3 4s2 4p6 4d10 4f14 4

Sec 4.2 Practice Problems 2. How many orbitals are in the following sublevels? a. 1s sublevel e. 4f sublevel b. 5s sublevel f. 7s sublevel c. 3p sublevel g. 6d sublevel d. 4d sublevel h. fourth principal energy level 1 7 1 1 3 5 5 16

Sec 4.2 Assignments Ch 4 Vocabulary 4.2 Study Guide (1-50) handout

End of Section 4.2