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Chapter 6 – Electron Structure of Atoms. Homework: 1, 2, 9, 10, 14, 15, 17, 19, 21, 23, 25, 28, 30, 31, 34, 35, 37, 39, 41, 42, 44, 47, 49, 51, 53, 55, 57, 58, 59, 60, 61, 62, 64, 66, 67, 70, 71, 72, 74, 78, 90. 6.1 – The Wave Nature of Light.
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Chapter 6 – Electron Structure of Atoms Homework: 1, 2, 9, 10, 14, 15, 17, 19, 21, 23, 25, 28, 30, 31, 34, 35, 37, 39, 41, 42, 44, 47, 49, 51, 53, 55, 57, 58, 59, 60, 61, 62, 64, 66, 67, 70, 71, 72, 74, 78, 90
6.1 – The Wave Nature of Light • The light that we see is called visible light, and is an example of electromagnetic radiation. • Also called radiant energy, because it can carry energy through space. • Lots of types of electromagnetic radiation • visible light, radio waves, infrared, etc. • All types of electromagnetic radiation travel through a vacuum at a speed of 3.0x108 m/s • The speed of light (c)
Waves • Waves are periodic • Which means they repeat in regular intervals • The distance between two adjacent peaks (or troughs) in a wave is called the wavelength (λ, lambda) • The number of complete wavelengths (or cycles) that pass a certain point each second is called its frequency (ν, nu)
The relationship between speed, wavelength and frequency can be expressed as • c = νλ • Since all electromagnetic waves move at the speed of light, a high wavelength means a low frequency, and vice versa.
Frequency expressed in the units of cycles/second (s-1) • Also known as hertz (Hz) • Wavelength is in meters
Example • The yellow light given off by a sodium vapor lamp has a wavelength of 590 nm. What is the frequency of this radiation?
Workspace • c = λν • Remember nm = 10-9 m
Example • A laser used in eye surgery to fuse detached retinas produces radiation with a wavelength of 640.0 nm. • What is the frequency of this radiation?
6.2 – Quantized Energy and Photons • There are 3 phenomena we will deal with that are not explained by the wave model of light. • The emission of light from hot objects • Called blackbody radiation • The emission of electrons from metals on which light shines • Called the photoelectric effect • The emission of light from electronically excited gas atoms • Called the emission spectra
Hot Objects and the Quantization of Energy • When solid objects are heated, they emit radiation • The red glow of an electric burner • White light of a tungsten lightbulb • The wavelengths of the light radiated depends on the temperature • Red-hot object cooler than a white-hot object • In the late 19th century, physics could not explain these behaviors.
In 1900, Max Planck figured out how to handle this. • Assumed that energy can be either released or absorbed by atoms only in discrete “chunks” of some minimum size. • He called the smallest quantity of energy that can be emitted or absorbed as electromagnetic radiation a quantum.
Planck proposed that the energy E, of a single quantum equals a constant times the frequency of the radiation • E = hv • h = Planck’s constant, 6.626x10-34 J-s • According to Planck’s theory, matter is allowed to emit and absorb energy only in whole number multiples of hv • Such as hv, 2hv, 3hv and so on
If the quantity of energy emitted is 3hv, we say the atom emitted 3 quanta of energy. • Because the energies can be released only in specific amounts, we say that the allowed energies are quantized • Which means their values are restricted to certain amounts
Does this seem odd? • If so, think of stairs • You can only step on the stairs, not between them. • Energy can only come in certain amounts, not between those amounts. • Why don’t we notice this with more things? • Why do energy changes seem continuous, rather than quantized? • Because Planck’s constant is so small, so on a larger scale, it seems continuous, but only when you look at energy on a very small scale does it appear to be quantized.
The Photoelectric Effect and Photons • In 1905, Albert Einstein used Planck’s quantum theory to explain the photoelectric effect. • When photons of sufficiently high energy strike a metal surface, electrons are emitted from the metal. • For each metal, there is a minimum frequency of light • If we go below that frequency, no electrons will be emitted.
Explaining Photoelectric Effect • To explain this, Einstein assumed that radiant energy striking the metal is acting like a stream of tiny particles (or energy packets), not like a wave. • He called each energy packet a photon. • Following Planck’s quantum theory, he decided each photon must have energy consistent with Planck’s equation • Energy of photon = E = hv
How This Works • Under the right conditions, a photon strikes a metal surface and is absorbed. • The photon can transfer its energy to an electron in the metal • A certain amount of energy (called the work function) is required for an electron to free itself from the metal • If the photon has less energy than the work function, the electron can’t escape from the metal surface. • If the photon has enough energy, electrons are emitted from the metal, the extra energy appearing as the kinetic energy of the emitted electrons.
6.3 Line Spectra and the Bohr Model • Planck and Einstein’s work opened up the doors for understanding how electrons are arranged in atoms. • In 1913, Danish physicist Niels Bohr came up with a theoretical explanation of line spectra
Line Spectra • A particular source of radiant energy may emit a single wavelength • Radiation composed of a single wavelength is called monochromatic • Common, most radiation sources produce radiation of many wavelengths. • When radiation from such sources is separated into its different wavelengths, a spectrum is produced.
Not all radiation sources produce a continuous spectrum. • When different gases are placed in a tube and a high voltage is applied, the gases will emit different colors of light. • When this light passes through a prism, only a few wavelengths are present in the resultant spetra.
The colored lines are separated by black regions • Black regions correspond to wavelengths that are absent from the light. • A spectrum containing radiation of only specific wavelengths is called a line spectrum
In 1885, a Swiss schoolteacher named Johann Balmer showed the wavelengths of the four (they couldn’t see others yet) visible lines of hydrogen fit a simple equation. • Balmer’s equation was later extended to a more general use and was called the Rydberg equation
Rydberg Equation • Allows us to calculate the wavelengths of all of the spectral lines of hydrogen • RH = Rydberg constant = 1.096776x107 m-1 • n1 and n2 are positive integers with n2 being larger than n1 • It took over 30 years to explain this equation
Bohr’s Model • Bohr refined Rutherford’s model of the atom, using Planck’s idea of quantized energy
Bohr’s Postulates • Only orbits of certain radii, corresponding to certain definite energies, are permitted for the electron in a hydrogen atom • An electron in a permitted orbit has a specific energy and is in an “allowed” energy state. An electron in an allowed energy state will not radiate energy and therefore will not spiral into the nucleus. • Energy is emitted or absorbed by the electron only as the electron changes from one allowed energy state to another. This energy is emitted or absorbed as a photon, E = hv
Energy States of the Hydrogen Atom • Bohr calculated the energies corresponding to each allowed orbit for the electron in the hydrogen atom • These energies fit the following formula • h = Planck’s constant • c = speed of light • RH = Rydberg constant
What about n? • The integer n, which can be between 1 and ∞, is called the principal quantum number • Each orbit corresponds to a different value of n • Radius gets larger as n increases. • So first orbit has n = 1 (closest) • Next allowed orbit has n = 2, and so on • The electron in a H atom can be in any allowed orbit, and the previous equation tells us the energy that the electron will have, depending on its orbit.
The energies of the electron in a hydrogen atom will always be negative • The lower (more negative) the energy is, the more stable the atom will be. • The energy is lowest (most negative) for n = 1 • This lowest energy state (n = 1) is called the ground state of the atom. • When the electron is in a higher (less negative) orbit, the atom is said to be in an excited state.
What happens…. • …to the orbit radius and energy as n becomes infinitely large? • The radius increases as n2, so we reach a point where the electron is completely separated from the nucleus. • When n = ∞, E = 0
So the state in which the electron is removed from the nucleus is the reference, or zero-energy, state of the hydrogen atom. • This zero-energy state is higher in energy than the states with negative energies.
In his 3rd postulate, Bohr assumed an electron could “jump” from one allowed energy state to another by absorbing or emitting photons • The photons’ energy must meet exactly the energy difference between the states • Or, radiant energy is emitted when the electron jumps to a lower energy level.
In equation form… • ΔE = Ef – Ei = Ephoton = hv • Substituting the previous energy equation into this one, and remembering that v = c/λ • ni and nf are the principal quantum numbers of the initial and final state of the atom. • If nf is smaller than ni, the electron moves closer to the nucleus, and ΔE is a negative number (atom loses energy)
Example • An electron moves from the 3rd principal quantum number to the 1st principal quantum number. What is the ΔE of this change? • First off: Should we expect our ΔE to be positive or negative? • Which quantum number is nf and which is ni? • nf = 1, ni= 3
ΔE = -2.18x10-18 (1-1/9) = -2.18x10-18(8/9) ΔE = -1.94x10-18 J
What is the wavelength of this photon? • λ = 1.03x10-7 m • Remember: • ΔE = hc/λ • What happened to the – sign? • Wavelength and frequency are always positive, so negative sign is ignored.
Shortcut equation • If we solve • for 1/λ, we find an equation remarkably similar to the Rydberg equation
Limitations • The Bohr model explains the line spectrum of hydrogen, but not the spectra of other atoms accurately. • But the Bohr model did bring in two important ideas into our model of the atom • Electrons exist only in certain discrete energy levels • Energy is involved in moving an electron from one level to another
6.4 The Wave Behavior of Matter • Following Bohr’s model for the hydrogen atom, the dual nature of radiant energy become a familiar concept. • Depending on the experiment, radiation appears to have either a wavelike or particle-like nature • Louis de Broglie extended this idea dramatically
De Broglie • If radiant energy could behave as a stream of particles, could matter behave like a wave? • Suppose the electron orbiting a nucleus wasn’t thought of as a particle, but a wave with a particular wavelength. • De Broglie suggested that it’s motion around a nucleus was associated with a particular wavelength. • He went on to propose that the particular wavelength of the electron, or of any other particle depended on its mass and velocity
De Broglie’s Equation • The quantity mv for any object is called its momentum (p) • h is Planck’s constant • De Broglie used the term matter waves to describe the wave properties of matter
What this means… • Because de Broglie’s hypothesis applies to all matter, any object with mass and velocity creates a characteristic matter wave. • However, the larger the mass, the smaller the wavelength. • Most ordinary objects have a wavelength so small as to be completely out of the range of any possible observation. • Electrons are so small though, that they will still have an applicable wavelength
Example • What is the wavelength of an electron moving with a speed of 5.97x106 ms? • The mass of an electron is 9.11x10-28 g • Note: de Broglie’s equation works only if • mass is in kg • velocity is in m/s
Workspace • h = 6.63x10-34
Use of this? • Used in electron microscopes
The Uncertainty Principle • Werner Heisenberg proposed that the dual nature of matter places a limitation on how precisely we can know the location and the momentum of any object. • This only really comes into play with matter on the subatomic level • This principal is called the uncertainty principal
