Atomic Structure Chapter 6

6.1 Electromagnetic Radiation All forms of radiation (such as light, microwaves, radio) are forms of energy that can be described in a mathematical theory called electromagnetic radiation. The distance between successive crests of a wave (or between successive troughs) is the wavelength of a wave. Wavelength is symbolized by λ (lambda) and usually measured in meters or nanometers.

Wave Properties Frequency is the number of wavelengths (or cycles) that pass a given point in a second. It is symbolized by ν (nu). number of events per time unit of s-1 (1 per second) or Hz (hertz)

Wave Properties Wave height is called amplitude and points of zero amplitude are called nodes. Nodes occur at intervals of λ/2. Speed of a wave can be calculated by multiplying wavelength times frequency. C = λν where C is the speed of light (3.0 x 108 m/s)

Electromagnetic Spectrum The electromagnetic spectrum includes all the wavelengths of radiant energy from short gamma rays to long radio waves. The visible spectrum is the part of the spectrum visible to the eye, usually with wavelengths between 400 and 700 nm.

Example Problem The wavelength of the radiation which produces the yellow color of a sodium vapor light is 589.0 nm. What is the frequency of radiation? Orange light has a _____ frequency and a _____ wavelength than blue light. (see page 271)

6.2 Planck, Einstein, Energy and Photons Before Planck, predictions to describe the relationship between wavelength and radiation failed in the ultraviolet region. Max Planck introduced the concept of quantized vibrations. Quantization means that only certain vibrations (specific frequencies) are allowed.

Planck, Einstein, Energy and Photons A quantum (or photon) is a particle of light energy that can be absorbed (or emitted) by a molecule. The energy of that molecule is increased (decreased) by an amount equal to the energy of the photon. Planck’s constant is a proportionality constant that describes the energy of a photon. E = hv where E is energy (J), h is Planck’s constant (J∙s), and v is frequency (s-1)

Planck, Einstein, Energy and Photons Light can cause chemical reactions to occur! (paint fades, cloth decomposes) As frequency increases, energy of radiation increases. Energy also increases as the wavelength decreases. E = hv = (hc)/λ (example: UV light has more energy than visible light due to shorter wavelengths)

Planck, Einstein, Energy and Photons higher intensity of light would mean there are more photons to strike a surface per unit of time photons have to have enough energy to remove electrons from an atom once the minimum energy (light frequency) is exceeded, the photons have enough energy to displace electrons more high energy photons means more electrons displaced

ν = c/λ E = hν E = hc/λ λ = wavelength in nm V = frequency in 1/s or Hz E = energy of a single photon in joules C = speed of light = 3.00 x 1017 nm/s h = Planck’s constant = 6.63 x 10-34 J-s

Planck, Einstein, Energy and Photons The photoelectric effect occurs when light strikes the surface of a metal and electrons are ejected. Einstein combined Planck’s equation with the concept of photons, the “particles” of light. Electromagnetic radiation is thought of a stream of photons. Matter is allowed to emit or absorb energy only in discrete amounts.

Practice Problem What is the frequency, the energy of a single photon, and the energy of a mole of photons of light having a wavelength of 555 nm?

Practice Problem Calculate (a) the energy in joules of a photon emitted by an excited sodium atom (wavelength 600 nm) and (b) the energy in kJ of a mole of photons.

Homework After reading sections 6.1 and 6.2, you should be able to do the following… p. 297 (3-12)

6.3 Atomic Line Spectra and Niels Bohr A spectrum that consists of light of all wavelengths is called a continuous spectrum. A line emission spectrum (or atomic emission spectrum) occurs when light from excited electrons emit only certain wavelengths of light. Each element produces a characteristic and identifiable pattern.

Line Emission Spectra Hydrogen’s series of 4 lines is referred to as the Balmer series.

Bohr Model Niels Bohr connected the emission spectra with Planck and Einstein’s ideas. Bohr proposed that electrons move in circular, fixed energy orbits around the nucleus. Each circular orbit corresponds to a stable energy state. Bohr introduced quantization into electronic structure!

Bohr Model An atom with electrons in the lowest possible energy levels is said to be in its ground state. When the electron of a hydrogen atom occupies an orbit with n greater than 1, it is said to be excited state.

Bohr Model Energy (a photon) is emitted or absorbed by an electron when it changes from one allowed energy state to another. The lines of the atomic emission spectrum of hydrogen result when an electron falls from a higher allowed state to a lower allowed state. The increment between each allowed state is proportional to Planck’s constant, the speed of light, and the Rydberg constant, RH.

Atomic Line Spectra The Rydberg equation allows us to calculate the wavelengths of different lines in the visible emission spectra of hydrogen atoms. You can use the Rydberg constant and Planck’s constant to calculate the energy states at different levels. where R = 1.0974 x 107 m-1

Practice Problem Calculate the energies of the n = 3 states of the hydrogen atom in joules per atom and in kilojoules per mole.

Bohr Theory and Spectra Electrons stay in lower energy levels unless they absorb or evolve energy due to some disturbance. Electrons in the ground state have energy with a large negative value. As the electron absorbs energy and moves to a higher energy level, its energy becomes less negative. positive change in energy – absorption negative change in energy – emission

Bohr Theory and Spectra As electrons naturally move back to lower levels, they emit energy which is observed as light. This is the atomic emission spectrum! The movement of electrons between quantized energy states. Bohr’s model only applies to H atoms or systems with one electron.

6.4 Particle Wave Duality Louis Victor de Broglie proposed that matter, such as an electron, could exhibit wavelike properties. He said that an electron with mass (m) moving with velocity (v) should have a wavelength… λ = h/(mv) Electrons were experimentally shown to be diffracted (like light waves) by a thin sheet of foil, so therefore electrons can have wave properties.

Practice Problem Calculate the wavelength associated with an electron of mass m = 9.109 x 10-28 g traveling at 60.0% of the velocity of light.

Homework After reading sections 6.3 and 6.4, you should be able to do the following… p. 298 (14-20,23-26)

6.5 Quantum Mechanical View The general approach to understanding atomic behavior that includes theories of Bohr, Schrodinger, and others is called quantum mechanics or wave mechanics. Like light, electrons have properties of both a wave and a particle. Werner Heisenberg concluded that it is impossible to fix both electron position and energy if the electron is described as a wave.

Heisenberg Uncertainty Principle The uncertainty principle, applied to electrons in an atom, states that it is inherently impossible to simultaneously determine exact position and momentum of an electron. The best that can be done is to predict probability of finding an electron in a certain region of space.

Schrodinger’s Model Erwin Schrodinger developed mathematical equations with solutions called wave functions (ψ – psi) that are chemically important. The square of a wave function is an orbital. orbital - probability of finding an electron of a given energy in a region of space (electron density)

Schrodinger’s Model The region of space in which an electron of a given energy is most probably located is called its orbital. Three integer numbers – the quantum numbers n, l, and ml – are an integral part of the mathematical solution.

Practice Questions Who proposed the wave-particle properties of electrons? Who discovered the charge-mass ratio of an electron? Who provided the theoretical explanation of the photoelectric effect? Who first postulated that the sharp lines in the emission spectra of elements were caused by electrons going from high energy levels to low energy levels?

Quantum Mechanical Model The quantum mechanical model of the atom is a mathematical model that incorporates both wave and particle characteristics of electrons in atoms.

Homework After reading section 6.5, you should be able to do the following… p. 299 (34-38) – needs to be adjusted for quantum numbers!

6.6 Shapes of Atomic Orbitals Electrons with the highest value of n are valence electrons.

s - orbital electrons cluster around the nucleus most of the time (probabilty is that electrons will be found within that radius about 90% of the time) – electron cloud picture electron density is greater closer to nucleus square of wave function (Ψ2) is probability density – high for points around nucleus s orbital is spherical in shape the size of s orbitals and their energy increases as n increases

p - orbitals All p orbitals have a nodal surface that slices through the nucleus and divides the region of electron density in half dumbbell shaped 3 possible orientations

d - orbitals Orientation possibilities are equal to the number of nodal surfaces that slice through the nucleus 2 nodal surfaces divides into four regions of electron density 5 d orbitals

f - orbitals seven orbitals 7 regions of electron density

6.7 Electron Spin Electrons have an intrinsic property known as spin that can result in atoms having a magnetic moment. At most, two electrons can be accommodated in an orbital, and these electrons must have opposite spin.

Magnetism Electrons act as “micromagnets”, and there are only two spins possible… A material that is slightly repelled by a strong magnet is said to be diamagnetic, materials that are attracted to a strong magnet are paramagnetic; they lose their magnetism once removed from the field. Ferromagnetic materials retain magnetism upon introduction to removal from a magnetic field.

Magnetism How can we account for the fact that the H atom is paramagnetic and the He atom is diamagnetic?

Atomic Orbitals and Chemistry By thinking about orbitals of atoms in molecules, and by making simple assumptions that they resemble those of the hydrogen atom, we can understand much of the chemistry of complex systems.