5.3 Physics and the Quantum Mechanical Model Electrons in Atoms 5.3 Physics and the Quantum Mechanical Model

Chemistry Today we are learning to:- 1. Understand the relationship between the wavelength and frequency of light 2. Understand the reasons for emission spectra 3. Explain how frequencies of emitted light are related to changes in electron energy 4. Distinguish between quantum mechanics and classical mechanics

Light How are the wavelength and frequency of light related? The amplitude of a wave is the wave’s height from zero to the crest. The wavelength, represented by  (the Greek letter lambda), is the distance between the crests.

Light How are the wavelength and frequency of light related? The frequency, represented by  (the Greek letter nu), is the number of wave cycles to pass a given point per unit of time. The SI unit of cycles per second is called a hertz (Hz).

Light How are the wavelength and frequency of light related? The product of the frequency and wavelength always equals a constant (c), the speed of light.

Light How are the wavelength and frequency of light related? The wavelength and frequency of light are inversely proportional to each other.

5.1 Sodium vapor lamps produce a yellow glow.

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What is the frequency of radiation with a wavelength of 5.00 x 10-8 m? What is the wavelength of radiation with a frequency of of 5.00 x 1015 Hz? Knowns c = 2.998 x 108 m/s λ = 5.00 x 10-8 m   c = λν therefore ν = c/λ ν = 2.998 x 108 m/s = 6.00 x 1017 s-1 5.00 x 10-8 m Knowns c = 2.998 x 108 m/s ν = 5.00 x 1015 s-1   c = λν therefore λ = c/ν λ = 2.998 x 108 m/s = 6.00 x 10-6 m 5.00 x 1015 m

for Sample Problem 5.1 An inexpensive laser that is available to the public emits light that has a wavelength of 650nm. What is the frequency of the radiation. Remember  1nm = 1 x 10-9m (check on page 74 of text book for SI units) Knowns c = 2.998 x 108 m/s λ = 650nm = 6.50 x 10-7 m   c = λν therefore ν = c/λ ν = 2.998 x 108 m/s = 4.61 x 1014 s-1 6.50 x 10-7 m

5.3 Atomic Spectra Atomic Spectra When light from a helium lamp passes through a prism, discrete lines are produced The frequencies of light emitted by an element separate into discrete lines to give the atomic emission spectrum of the element.

5.3 Atomic Spectra Atomic Spectra In the Bohr model: When the electron has its lowest possible energy, the atom is in its ground state. Excitation of the electron by absorbing energy raises the atom from the ground state to an excited state. A quantum of energy in the form of light is emitted when the electron drops back to a lower energy level.

An Explanation of Atomic Spectra 5.3 An Explanation of Atomic Spectra Atomic Spectra The three groups of lines in the hydrogen spectrum correspond to the transition of electrons from higher energy levels to lower energy levels. The three groups of lines in the hydrogen spectrum correspond to the transition of electrons from higher energy levels to lower energy levels. The Lyman series corresponds to the transition to the n  1 energy level. The Balmer series corresponds to the transition to the n  2 energy level. The Paschen series corresponds to the transition to the n  3 energy level.

5.3 Atomic Spectra Quantum Mechanics Main points: (1905 Special Relativity Theory) Einstein showed that light could be described by packets of energy (quanta) called photons. (1924) DeBroglie developed an equation that predicts that all moving particles have wavelike behavior (Ex. electrons). This is called ‘the wave particle duality of matter’. (λ = h/p = h/mv) The wavelike properties of electrons are used in electron microscopes They have much smaller wavelengths than visible light, and can give greater magnification.

5.3 Atomic Spectra Quantum Mechanics Main points: Classical mechanics describes the motions of bodies much larger than atoms, while quantum mechanics describes the motions of subatomic particles and atoms as waves. The Heisenberg uncertainty principle states that it is impossible to know exactly both the velocity and the position of a particle at the same time.

The Heisenberg Uncertainty Principle

5.3 Section Quiz. 1. Calculate the frequency of a radar wave with a wavelength of 125 mm. 2.40 109 Hz 2.40 1024 Hz 2.40 106 Hz 2.40 102 Hz

2. The lines in the emission spectrum for an element are caused by 5.3 Section Quiz. 2. The lines in the emission spectrum for an element are caused by the movement of electrons from lower to higher energy levels. the movement of electrons from higher to lower energy levels. the electron configuration in the ground state. the electron configuration of an atom.

5.3 Section Quiz. 3. Spectral lines in a series become closer together as n increases because the energy levels have similar values. energy levels become farther apart. atom is approaching ground state. electrons are being emitted at a slower rate.

2.3 Vocabulary 5.1 Vocabulary 5.2 Vocabulary 5.4 Vocabulary Energy levels: possible electron orbits in Bohr’s model of the atom Quantum: small whole number unit of energy Quantum mechanical model: quantum description of the movement of electrons in atoms obtained from solving Schrodinger’s equations Atomic orbital: region of space where there is a high probability of finding an electron 5.2 Vocabulary Electron configuration: knocks electrons of atoms to produce ions Aufbau principle: Electrons occupy orbitals of lowest energy first. Pauli exclusion principle: Atomic orbitals can hold up to 2 electrons of opposite spin. Hunds rule: All orbitals of the same energy must have an electron in them before they can pair up. 5.4 Vocabulary Amplitude: waves height from the origin. Wavelength: distance between crests. Frequency: number of waves passing a given point per second. Hertz: S.I. Unit of frequency 1 Hz = 1s-1 = 1 1/s = 1 cycle per second. Electromagnetic radiation: Radiation over a broad band of wavelengths. Spectrum: The result of light being split into its component colors. Atomic emission spectrum: Spectrum from the light emitted by an element. Ground state: Lowest energy state of an electron in an atom. Photons: Quanta of light particles Heizenberg uncertainty principle: You can’t find the position and velocity of a particle simultaneously

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