2 Quantum Model: Chapter 4 Lesson 2

Bohr Model:

1. describes electrons in terms of their energy state

a) lowest total energy occurs when it is closest to the nucleus "ground state"

b) the state in which it has higher energy than at ground state "excited state"

2. describe definite orbits occupied by electron particles

3. electrons circle the nucleus in allowed path called orbits

a) orbits are separated by a large space in which electrons cannot exist

b) electrons can be in 1 orbit or another but not in between

4. Line spectrum is produced when an electron drops from a higher energy orbit to a lower energy orbit

Bohr Model Introduced:

1. different energy levels

2. electrons orbit the nucleus

3. explained the electrons can move certain distances from the nucleus

4. explained electrons move with only certain speeds

5. explains a simple Hydrogen atom, but it does not work for more complex atoms

Heisenberg:

1. stated it is impossible to know both the exact position and the exact momentum of an object at the same time

2. to locate the exact position we must be able to look at it

3. believed it is impossible to determine an electron path without changing that path

4. Heisenberg uncertainty principle: states there is always some uncertainty about the position and momentum of an electron

5. treats the electron as a particle

de Broglie

1. was inspired by the dual-wave particle nature of light

2. electrons have a wave-particle nature

3. treated electron particles as waves

Schrodinger:

1. impressed by de Broglie devised an equation that treated electrons moving around nuclei as waves

2. wave equation laid the foundation of Quantum Theory

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

4. mathematical equation that fits all atoms

5. states the nucleus is not surrounded by orbits, but orbitals (a 3D region about the nucleus in which a particular electron can be located)

6. treats electrons as waves that have only certain probability of being found at various distances

QUANTUM NUMBERS

DEFINITION:SPECIFY THE PROPERTIES OF ATOMIC ORBITALS AND THE PROPERTIES OF ELECTRONS IN ORBITALS

• HELPS TO DESCRIBE THE ORBITALS

• THE FIRST THREE RESULT FROM SCHRODINGER’S EQUATION

• THE FOURTH DESCRIBES A FUNDAMENTAL STATE OF THE ELECTRON THAT OCCUPIES THE ORBITAL

Quantum Numbers

1. Principal Quantum Number:

a) symbolized by n

b) Indicates the main energy level occupied by the electron

c) As n increases, the electron’s energy and its average distance from the nucleus increase

d) indicates the cloud size, the larger the number the bigger the cloud

e) greatest number of electrons in any one level is 2n²

2. Angular Momentum Quantum Number:
a) indicates the shape of the cloud

b) symbolized by l

c) describes the shapes as sublevels within an energy level

d) the number of sublevels within an energy level equals the value of the principle quantum number of that level

e) the space occupied by one pair of electrons is called an orbital

f) indicated as s, p, d, f

g) s is the lowest in energy, and increases in energy with p, d, and f

3. Magnetic Quantum Number:

a) indicates the orientation in space of the cloud

b) symbolized by m

c) indicates the position of the orbitals about the 3 axis (x, y, z)

d) each orbital can hold a pair of electrons

e) used to distinguish between orbitals that are within the same sublevel

f) indicates direction in space

g) s has 1 position, p has 3 positions, d has 5 positions, f has 7 positions

4. Spin Quantum Number:

a) distinguishes between electrons in the same orbital

b) describes the spin of the electron

c) spin clockwise or counterclockwise direction

key concepts from the provided text on atomic models and quantum mechanics:

Briefing Document: Atomic Structure and Quantum Theory

Introduction:

This document summarizes key concepts in the development of atomic models, moving from the early Bohr model to the more sophisticated quantum mechanical model. It highlights the evolution in understanding of electron behavior and the introduction of wave-particle duality. Finally, it delves into the quantum numbers used to describe electron behavior.

1. The Bohr Model:

• Key Concept: The Bohr model introduces the idea of electrons existing in specific energy levels.

• Energy States: Electrons are described in terms of their energy states.

• "lowest total energy occurs when it is closest to the nucleus 'ground state'".

• "'excited state' the state in which it has higher energy than at ground state"

• Orbits: Electrons are thought to orbit the nucleus in fixed, defined paths.

• "electrons circle the nucleus in allowed path called orbits"

• "orbits are separated by a large space in which electrons cannot exist"

• "electrons can be in 1 orbit or another but not in between"

• Line Spectra: The model explains line spectra as a result of electrons transitioning between orbits.

• "Line spectrum is produced when an electron drops from a higher energy orbit to a lower energy orbit"

• Limitations: While successful for the simple hydrogen atom, the Bohr model fails to accurately describe more complex atoms.

• "explains a simple Hydrogen atom, but it does not work for more complex atoms"

2. Heisenberg's Uncertainty Principle:

• Key Concept: It is impossible to simultaneously know the exact position and momentum of an electron.

• Measurement Problem: Locating an electron requires observing it, which inevitably alters its path.

• "to locate the exact position we must be able to look at it"

• "believed it is impossible to determine an electron path without changing that path"

• Uncertainty: "Heisenberg uncertainty principle: states there is always some uncertainty about the position and momentum of an electron"

• Particle Nature: The principle treats the electron as a particle.

• Implication: Challenges the idea of fixed orbits and introduces uncertainty in describing electron behavior

3. de Broglie's Wave-Particle Duality:

• Key Concept: Electrons exhibit both wave-like and particle-like characteristics, drawing inspiration from the wave-particle duality of light.

• Dual Nature: "electrons have a wave-particle nature"

• Treatment of Electrons: "treated electron particles as waves"

4. Schrodinger's Quantum Model:

• Key Concept: Treats electrons as waves and introduces the concept of orbitals, regions of probability rather than defined orbits.

• Wave Equation: Schrodinger developed "an equation that treated electrons moving around nuclei as waves"

• This "wave equation laid the foundation of Quantum Theory" and provides a "mathematical equation that fits all atoms"

• Probability: Rather than fixed paths, electrons are described by "mathematical equation that fits all atoms" where there is only a "certain probability of being found at various distances".

• Orbitals: The nucleus is "not surrounded by orbits, but orbitals (a 3D region about the nucleus in which a particular electron can be located)".

• Quantum Theory: "Quantum theory describes mathematically the wave properties of electrons and other very small particles"

5. Quantum Numbers:

• Definition: Quantum numbers "SPECIFY THE PROPERTIES OF ATOMIC ORBITALS AND THE PROPERTIES OF ELECTRONS IN ORBITALS" and are used to describe the characteristics of electron orbitals and the electrons within them.

• Origin: The first three result from Schrodinger’s Equation. The fourth describes a fundamental state of the electron.

• Types of Quantum Numbers:Principal Quantum Number (n):Symbolized by 'n'.

• Indicates the main energy level of the electron.

• As 'n' increases, the electron's energy and average distance from the nucleus increases.

• "indicates the cloud size, the larger the number the bigger the cloud"

• "greatest number of electrons in any one level is 2n2"

• Angular Momentum Quantum Number (l):Symbolized by 'l'.

• Indicates the shape of the electron cloud (orbital).

• Describes sublevels within an energy level.

• "the number of sublevels within an energy level equals the value of the principle quantum number of that level"

• The space occupied by a pair of electrons is called an orbital

• Sublevels are identified as s, p, d, and f.

• "s is the lowest in energy, and increases in energy with p, d, and f"

• Magnetic Quantum Number (m):Symbolized by 'm'.

• Indicates the spatial orientation of the orbital

• Describes the position of the orbital on the x,y,z axis

• Each orbital can hold a pair of electrons

• Distinguishes between orbitals in the same sublevel

• "s has 1 position, p has 3 positions, d has 5 positions, f has 7 positions"

• Spin Quantum Number:Distinguishes between the two electrons in the same orbital.

• Describes the spin of the electron, either clockwise or counterclockwise.

Conclusion:

The evolution of atomic models, moving from the Bohr model to the quantum mechanical model, reflects a significant shift in understanding of the nature of electrons. The introduction of concepts like wave-particle duality, the uncertainty principle, and the use of quantum numbers has allowed for a more accurate and complete picture of atomic structure and behavior. While the Bohr model provided a starting point, it was Schrodinger’s work and the development of the quantum numbers that enabled accurate descriptions of atoms and their behaviors.

timeline of the main events and a cast of characters based on the provided text:

Timeline of Main Events

1. Bohr's Model of the Atom is Introduced: This model introduces the concept of electrons orbiting the nucleus in specific paths (orbits) at definite energy levels. It explains the behavior of simple atoms like Hydrogen, and the production of line spectra as electrons move between these energy levels. The model specifies that electrons occupy allowed orbits separated by large spaces. Electrons can exist in one orbit or another, but not in between. Electrons orbit the nucleus with certain speeds.

2. Heisenberg's Uncertainty Principle: Heisenberg proposes that it is fundamentally impossible to simultaneously know the exact position and momentum of a particle, particularly an electron. This is due to the act of observation changing its path. The principle introduces the idea of inherent uncertainty in the properties of subatomic particles.

3. de Broglie's Hypothesis: Inspired by the wave-particle duality of light, de Broglie proposes that electrons also exhibit wave-like properties in addition to their particle nature.

4. Schrödinger Develops the Wave Equation: Building on de Broglie's ideas, Schrödinger develops a mathematical equation to describe the behavior of electrons as waves around the nucleus. This equation forms the foundation of Quantum Theory. It also implies that electrons exist in orbitals (3D regions), not orbits. Electrons are treated as waves that have a probability of being found at various distances.

5. Quantum Numbers are Defined: A set of four quantum numbers are established to specify the properties of atomic orbitals and the electrons within them. These numbers help describe the size, shape, orientation, and spin of the electron cloud and the electrons:

• Principal Quantum Number (n): Describes the energy level and size of the electron cloud.

• Angular Momentum Quantum Number (l): Describes the shape of the electron cloud (sublevels s, p, d, f).

• Magnetic Quantum Number (m): Describes the orientation of the electron cloud in space.

• Spin Quantum Number: Describes the spin of the electron (clockwise or counterclockwise).

Cast of Characters

• Niels Bohr: Developed an early atomic model that proposed electrons orbit the nucleus in specific paths with definite energy levels and speeds. He introduced the concept of ground and excited states. However, his model was only effective with simpler atoms like Hydrogen.

• Werner Heisenberg: Formulated the uncertainty principle, which states that it is impossible to know both the exact position and the exact momentum of a subatomic particle simultaneously. He believed the act of observation influences the path of an electron, making it impossible to map without altering its path. He treated the electron as a particle.

• Louis de Broglie: Proposed the concept that electrons have a dual wave-particle nature. He treated the electron as a wave. This inspired Schrodinger and the wave equation.

• Erwin Schrödinger: Developed the wave equation, a mathematical description of the behavior of electrons as waves around the nucleus, laying the foundation for Quantum Theory. He proposed that the electron exists in a 3D space around the nucleus called an orbital.