Chemistry 1A - Foothill College

Electronic Structure of Atoms (Quantum Theory) Classical Theory: By the early 1900’s, “classical theory” viewed light as behaving like a wave (can be diffracted for instance) and electrons as behaving like particles (have mass and momentum for instance). Classical physics also viewed energy as continuous, meaning that all values of energy are allowed. However, certain experimental observations could not be explained using classical physics. These included the distribution of light that is given off from a glowing hot object (like a light bulb filament or an electric stove), the photoelectron effect and atomic emission spectra. During the early 1900’s a bold new theory, quantum theory was proposed as a way to explain these.

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Your goals in studying this chapter are to: • • • • • • • • • • • • • • • •

develop an understanding of and be able to describe the properties of electromagnetic radiation, EMR understand the relationship between frequency, wavelength and energy of EMR; be able to calculate one from another understand what is meant by wave-particle duality understand and be able to describe what the photoelectric effect is understand and be able to describe the emission of light from atoms understand and be able to describe the Bohr model of the hydrogen atom and its historical significance; be able to mathematically relate the wavelength of emitted light to energy levels in the hydrogen atom be able to draw an energy level diagram for an H atom (1 electron system) be able to draw an energy level diagram for all other atoms atom (2 or more electron systems); understand in what ways and why energy diagrams for all other atoms are different compared to the hydrogen atom. be able to define the three quantum numbers: n, l, ml and their relation to atomic orbital energy and shape. be able to draw the shape of s and p orbitals. understand the “4th” quantum number, ms understand and be able to describe what an orbital is. understand and be able to sketch the radial probability function for s orbitals. understand and be able to describe the Pauli exclusion principle. understand and apply the Aufbau principle and Hund’s rule for electron filling of energy levels. write orbital box diagrams and electron configurations for elements that follow the expected filling order. Know the exceptions for the first row d elements. Electronic Structure

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Chemistry 1A - Foothill College

Electromagnetic Radiation (Light) •

Remember that Rutherford discovered the nuclear nature of the atom by bombarding thin sheets of metal foil with relatively massive α particles. From his experiment, he concluded that the electrons in an atom are located in a region surrounded a very tiny, dense nucleus that contains most of the atom’s mass. However, he could not describe the arrangement of the electrons, the electronic structure. In order to determine the electronic structure of the atom we need something less brutal than the relatively massive α particles Rutherford used. We use electromagnetic radiation to do this.

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Electromagnetic radiation consists of oscillating (wavelike) electric and magnetic fields that can propagate over large distances through empty space. Since it is a wave, electromagnetic radiation exhibits properties associated with waves. For instance, it can be diffracted. Electromagnetic radiation originates from the movement of electrons in atoms, molecules and ions. Thus, through the study of the electromagnetic radiation absorbed or emitted by atoms, molecules and ions we can learn something about the arrangement of electrons in atoms, molecules and ions. We will focus on atoms here.

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Electromagnetic Radiation • Electromagnetic radiation, EM, can be described as alternating electric and magnetic vectors. • Each wave has an amplitude, energy, frequency, wavelength, and a propagation speed. • The relationship between wavelength, λ, frequency, ν, and speed, c is: λ x ν = c = 2.998x108 m/s (in a vacuum) • λ is measured in m, while ν is measured in hertz (Hz): 1 Hz = 1 cycle/s = 1/s • What is the frequency of light with a wavelength of 435 nm?

Electronic Structure

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Chemistry 1A - Foothill College

Visible Spectrum of EM • •

As wavelength decreases, frequency increases, and energy also increases. Electromagnetic radiation extends continuously across a spectrum from the shortest wavelength (highest frequency) to the longest wavelength (lowest frequency).

ν = c/λ

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What we perceive as white light is electromagnetic radiation consisting of all the colors of visible light. Electronic Structure

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Planck and Quantized Energy (The Birth of Quantum Theory!) When heated, solids emit electromagnetic radiation. Tungsten filament light bulbs and electric stoves are examples of this phenomenon. The wavelength distribution of the radiation depends upon the temperature and the distribution cannot be explained using classical physics where energy is viewed as being “continuous”, all values “allowed”.

Electronic Structure

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Chemistry 1A - Foothill College

Planck’s Proposed Explanation In 1900, the German physicist Max Planck (1918 Noble Prize in Physics) was able to explain the distribution of light emitted by a hot, glowing object by assuming that energy comes in tiny packets; Planck gave the name quantum, meaning “fixed amount”, to the tiny packets of energy that are emitted or absorbed as electromagnetic radiation. He proposed that the energy of a single quantum is proportional to the frequency of the radiation emitted: E = hν

h = 6.626 x 10–34 Js

where the proportionality constant (h) is called “Planck’s constant”. Planck further proposed that electromagnetic energy can be absorbed or emitted only in quantized form as discrete “chunks” of energy corresponding to whole-number multiples of hν, such as hν, 2hν, 3hν, and so on. WOW! Planck’s proposal means that energy is not continuous as classical theory assumed, energy is quantized, meaning that it is restricted to certain quantities.

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Planck’s Equation Quantized Energy and What We Now Understand • Planck’s equation shows that energy of emitted light from a heated source is “quantized”. The quantization comes from the allowed frequencies of vibration of the heated atoms. (Unknown to Planck at the time!) E (energy, J) = n(hν) where n is a positive integer called a quantum number, h = Planck’s constant = 6.626x10-34 J•s and ν is the frequency of vibration. • Each “allowed” vibrational frequency emits quantized light; light of a specific energy. • At any given temperature a distribution of vibrational frequencies is possible, hence a distribution of emitted light. • As temperature increases, the distribution shifts to higher energy vibrations, thus higher frequencies.

Electronic Structure

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Chemistry 1A - Foothill College

Einstein and Photons (The Birth of Quantum Theory!) Albert Einstein used Planck’s ideas to explain the photoelectric effect.

PhotoelectricEffect.MOV The photoelectric effect occurs when light strikes the surface of a metal causing electrons to be ejected from the metal. Experiments have shown that electrons are ejected only if the frequency of light is high enough. If lower frequency light is used, no electrons are ejected regardless of how intense the light is. Electronic Structure

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Einstein’s Proposed Explanation Einstein reasoned that the photoelectric effect is consistent with the idea that light can be thought of as being composed of tiny particles or packets of energy. Each particle has a given energy, E = hν, associated with it. One of these particles can”bump” an electron from the surface of the metal only if the particle has some minimum energy (minimum frequency). Einstein proposed that light has “particle-like” (momentum) properties. We now call these particles photons. Each photon has a specific energy depending upon its frequency (wavelength): E = hν In order for an electron to be ejected from the surface of a substance by a photon, the photon must have a certain minimum amount of energy or greater. Wording we now use: When a photon of sufficient energy is used, it transfers all of its energy to an electron enabling the electron to overcome the surface potential or what we call the “work function” of the metal. Work function refers to the minimum energy needed to remove an electron from a solid to a point immediately outside the solid surface. The work function is a characteristic property for any solid surface of a substance with a conduction band. (In simpler words, the work function is the minimum amount of energy needed in order for an electron in an metallic atom to escape to the surface of the metal.) Electronic Structure 10

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Chemistry 1A - Foothill College

Wave-Particle Duality •Electromagnetic radiation is said to have a wave-particle duality. It behaves like a wave (can be diffracted for example) as well as a particle (the photoelectric effect). WOW, NEAT! •Overall equation related energy, wavelength and frequency of light: Ephoton = hν = hc/λ Example Problem: Calculate the frequency in kilohertz of electromagnetic radiation with energy 3.71 x 10–28 J/photon.

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Example Problems Textbook Problem 6.29: Molybdenum metal must absorb radiation with a minimum frequency of 1.09 x 1015 s−1 before it can emit an electron from its surface via the photoelectric effect. (a) What is the minimum energy needed to produce this effect? (b) What wavelength radiation will provide a photon of this energy?

(c) If molybdenum is irradiated with light of wavelength of 120 nm, what is the maximum possible kinetic energy of the emitted electrons?

Electronic Structure

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Chemistry 1A - Foothill College

Example Problems Textbook Problem 6.82: The light-sensitive substance in black-and-white photographic film is AgBr. Photons provide the energy necessary to transfer an electron from Br- to Ag+ to produce Ag and Br and thereby darken the film. (a) If a minimum energy of 2.00 × 105 J/mol is needed for this process, what is the minimum energy needed by each photon?

(b) Calculate the wavelength of the light necessary to provide photons of this energy.

(c) Explain why this film can be handled in a darkroom under red light.

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Emission of Light Emission Spectrum: A figure showing the distribution of the wavelengths of electromagnetic radiation emitted by an object.

This figure illustrates a “continuous emission spectrum”. The electromagnetic radiation emitted from a light bulb or the sun are examples. Note that a “rainbow” or all wavelengths (energies) of light are observed, an observation consistent with “classical physics”. Electronic Structure

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Line Spectra of Some Elements - Observations that Lead to The Bohr Model of the Atom The light emitted by excited atoms IN THE GAS PHASE was found not to be continuous in energy like like a rainbow. Atomic emission spectra show a series of sharp lines at specific wavelengths. Each element has a unique emission spectrum. This phenomenon cannot be explained using classical physics.

Atomic emission spectra of hydrogen, mercury and neon:

FlameTestsforMetals.MOV

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