Chapter 13 Electrons in Atoms

Section 13.1 Models of the Atom Objectives: Summarize the development of atomic theory Explain the significance of quantized energies of electrons as they relate to the quantum mechanical model of the atom

Section 13.1 Models of the Atom Dalton Thomson Modern Rutherford Bohr

John Dalton’s Model Responsible for Atomic Theory in the early 1800’s Matter is made up of solid, indivisible particles This was before we knew about subatomic particles

J. J. Thomson’s Model Discovered electrons                                 Discovered electrons Had negatively charged electrons stuck into a lump of positively charged material “Plum-Pudding” model model explained some electrical properties of atoms

Ernest Rutherford’s Model Discovered the nucleus - dense positive center of the atom Electrons surrounded it Did not explain why electrons were not pulled into the nucleus “Nuclear model” Gold-Foil Test

Bohr’s Model Bohr suggested the electrons orbit the nucleus This is why atoms don’t collapse These orbits are like rungs on a ladder People can’t stand between rungs, and electrons can’t be between orbits Nucleus Electron Orbit Energy Levels

Bohr’s Model Energy levels – these are the orbits where an electron is likely to be Higher rungs mean higher energy Quantum – the amount of energy needed by an electron to move up an energy level There is no “in between” energy

Quantum Mechanical Model Erwin Schrodinger – physicist who wrote a mathematical equation describing the location and energy of electrons in atoms. This model makes estimations of where the electrons are likely to be The probability of finding an electron within a certain volume of space surrounding the nucleus can be represented as a fuzzy cloud. 90% chance electron is in the “fuzzy cloud”

Each Atom has 4 Quantum Numbers Used to specify the “address” of each electron in an atom. No two electrons have the same 4 quantum numbers. Principal Energy Level (n) Energy Sublevel (l) Atomic Orbital (m) Electron Spin (s)

Principal Energy Level (n) Principal Energy Level (n) – numbers used to show which principal energy level electrons in n= 1, 2, 3, 4, and so on Determine size of the orbital n2 = number of orbitals per main energy level 2n2 = number of electrons per main energy level Higher n, higher principal energy level, farther average distance from the nucleus

Energy Sublevel (l) s p d f s = 0 p = 1 d = 2 f = 3 Each principal energy level has energy sublevels associated with it. (l will always be at least one less than n) Theater seating (sections) # of sublevels in each energy level = n Ex: n=1 has sublevel 1s n=2 has sublevels 2s and 2p n=3 has sublevels 3s, 3p, and 3d Each sublevel has a letter associated with it and a number assigned to it. s = 0 p = 1 d = 2 f = 3 s p d f

Atomic Orbital (m) Each sublevel will have a certain # of orbitals (orientations in space). (-l ≤ m ≤ l) s = 1 p = 3 d = 5 f = 7

Spin Quantum Number (s) Each orbital can hold up to 2 electrons (of opposite spin).

Quantum Number Examples:

13.2 - Electron Configurations Objectives: Apply the aufbau principle, the Pauli exclusion principle, and Hund’s rule in writing the elctron cofigurations of elements Explain why the electron configurations for some elements differ from those assigned using the aufbau principle

13.2 - Electron Configurations Electron configurations – ways in which electrons are arranged around the nucleus Follow 3 rules to find configuration of element Aufbau principle, Pauli exclusion principle, and Hund’s rule Chlorine – 1s2 2s2 2p6 3s2 3p5

Electron Configuration Rules Aufbau principle – electrons enter sublevels of lowest energy first (p367) 4s is lower than 3d, so 4s is filled first Pauli exclusion principle – only 2 electrons can occupy each orbital (box) Electrons must have opposite spins Hund’s Rule – 1 electron goes in each orbital of the same energy sublevel until each orbital has an electron in it Spins of single electrons must be same

Electron Configurations

Examples

Configuration Exceptions Transition metals like to have a half filled or fully filled d sublevel. An electron may leave the s sublevel and go to the d sublevel to make it half or fully filled Cr – 1s2 2s2 2p6 3s2 3p6 4s2 3d4 incorrect Cr – 1s2 2s2 2p6 3s2 3p6 4s1 3d5 correct Cu – 1s2 2s2 2p6 3s2 3p6 4s2 3d9 incorrect Cu – 1s2 2s2 2p6 3s2 3p6 4s1 3d10 correct

Section 13.3 Physics and the Quantum Mechanical Model Objectives: Calculate the wavelength, frequency, or energy of light given two of these values Explain the origin of the atomic emission spectrum of an element

Light and Atomic Spectra According to the wave model, light consists of electromagnetic waves. Electromagnetic radiation includes: radio waves, microwaves, infrared waves, visible light, UV rays, x- rays and gamma rays. All electromagnetic waves travel in a vacuum at a speed of 3.00 x 108 m/s.

Parts of a transverse wave. A wave is a repeated, periodic oscillation

Waves The amplitude of a wave is the wave’s height from the origin to the crest. The wavelength (λ) is the distance between the crests. Frequency (ν) is the number of wave cycles to pass a given point per unit of time. Frequency in measure in hertz (Hz). A hertz is equivalent to an inverse second. Hz = s-1 c = λν Frequency and wavelength are inversely proportional. If one increases, the other will decrease. Amplitude will not affect wavelength or frequency.

Ex. Calculate the wavelength of light emitted by a lamp if the frequency is 5.10 x 1014 Hz.

Ex. Find the frequency of a wave if the wavelength is 5.00 x 10-6 cm.

When light travels through a prism, the different wavelengths separate into a spectrum of colors. These colors are referred to as visible light. ROY G BIV Red, Orange, Yellow, Green, Blue, Indigo, Violet Red has the longest wavelength and violet the shortest.

Every element emits light when it is excited by the passage of an electric discharge through its gas or vapor. Passing the light emitted by an element through a prism give the atomic emission spectrum of the element. The emission spectrum of each element is unique to that element. This makes is useful for the identification of unknown substances (i.e. composition of stars). The instrument used to obtain the emission spectra is called an emission spectrograph.

“Neon” lights Elements can by made to give off light by passing electricity through the gas state. The electricity excites electrons When electrons jump back down to a lower energy level, they emit energy (light).

The Quantum Concept and the Photoelectric Effect Max Planck began the idea that explained atomic spectra. (1900) Planck studied why a body, such as iron, appears to change color when heated (black, red, yellow, white, and blue). He assumed that the energy of a body changes only in small discrete units. Planck showed mathematically that the amount of radiant energy (E) is proportional to the frequency of the radiation (ν). E = hν Planck’s constant (h) has a value of 6.6262 x 10-34 Js.

Planck proposed that quanta of energy can be absorbed or emitted Planck proposed that quanta of energy can be absorbed or emitted. Albert Einstein followed this proposal. In 1905, Albert Einstein, proposed that light could be described as quanta of energy that behave as if they were particles. Light quanta are called photons, energy with no mass. The dual wave-particle nature was born, and scientists had difficulty accepting it. How can something act like a particle and light. It did explain the previously mysterious photoelectric effect.

Photoelectric Effect Photoelectric effect – metals eject electrons called photoelectrons when light shines on them. Alkali metals are particularly subject to the effect. Not just any frequency of light will cause the effect to occur. Depending on the element, the frequency will need to be elevated for this to occur. Certain metals work with certain frequencies Billiard ball analogy Applications in solar panels

Einstein used his particle theory of light to explain the photoelectric effect. Since E = hν, the higher the frequency, the more energy is emitted.

An Explanation of Atomic Spectra Bohr’s application of quantum theory to electron energy levels in atoms resulted in an explanation of the hydrogen spectrum. This was only partially satisfactory, since it only explained atoms and ions with one electron. Ground state is when an electron is in its lowest energy level. Excited state is when an electron is raised to an excited state, in an energy level with higher energy than originally in.

Quantum Mechanics De Broglie derived an equation that described the wavelength of a moving particle: λ = h/mν From this equation, it is easy to calculate the wavelength of a moving electron. This equation predicts that all matter exhibits wavelike motions.

De Broglie’s prediction that matter would exhibit both wave and particle properties set the stage for an entirely new method of describing the motions of subatomic particles, atom, and molecules. This is called quantum mechanics.

Summary of differences between classical and quantum mechanics. Classical mechanics adequately describes the motions of bodies much larger than the atoms that they comprise. It appears that such a body gains or loses energy in any amount. Quantum mechanics descries the motions of subatomic particles and atoms as waves. These particles gain or lose energy in packages called quanta.

Another feature of quantum mechanics not found in classical mechanics is the Heisenberg uncertainty principle. It is impossible to know exactly both the velocity and the position of a particle at the same time.

Strange things All objects exhibit wavelike behavior?! Your wavelength is too small to measure Heisenberg’s uncertainty principle

The Black Horseshoe Everything radiates The frequency of this radiation depends on the energy (temp) Don’t pick up any black horseshoes!