Chapter 6 Electronic Structure of Atoms
6.1 The Wave Nature of Light Made up of electromagnetic radiation. Waves of electric and magnetic fields at right angles to each other.
Parts of a wave Wavelength l Frequency = number of cycles in one second Measured in hertz 1 hertz = 1 cycle/second = s -1
Frequency = n
Kinds of EM waves There are many different l and n Radio waves, microwaves, x rays and gamma rays are all examples. Light is only the part our eyes can detect. Gamma Rays Radio waves
The speed of light in a vacuum is 2.998 x 10 8 m/s = c c = ln What is the wavelength of light with a frequency 5.89 x 10 5 Hz? What is the frequency of blue light with a wavelength of 484 nm?
In 1900 Matter and energy were seen as different from each other in fundamental ways. Matter was particles. Energy could come in waves, with any frequency. Max Planck found that as the cooling of hot objects couldn t be explained by viewing energy as a wave.
Hot Objects and the Quantization of Energy Planck found DE came in chunks with size hn DE = nhn where n is an integer. and h is Planck s constant h = 6.626 x 10-34 J-s these packets of hn are called quantum
The Photoelectric Effect - Einstein is next Light shining on a clean metal surface causes the surface to emit electrons. Said electromagnetic radiation is quantized in particles called photons. Each photon has energy = hn = hc/l Combine this with E = mc 2 You get the apparent mass of a photon. m = h / (lc)
You Try It Calculate the energy of one photon of yellow light whose wavelength is 589 nm.
Which is it? Is energy a wave like light, or a particle? Yes Concept is called the Wave -Particle duality. What about the other way, is matter a wave? Yes
Matter as a wave Using the velocity v instead of the wavelength n we get. De Broglie s equation l = h/mv Can calculate the wavelength of an object. The quantity mv for any object is called its momentum De Broglie used the term matter waves.
You Try It What is the wavelength of an electron moving with a speed of 5.97 x 10 6 m/s? The mass of an electron is 9.11 x 10-28 g.
Diffraction When light passes through, or reflects off, a series of thinly spaced line, it creates a rainbow effect because the waves interfere with each other.
15 A wave moves toward a slit.
16 Comes out as a curve
17 with two holes
with two holes Two Curves 18
with two holes Two Curves Interfere with each other 19
with two holes Two Curves Interfere with each other crests add up 20
21 Several waves
Several waves Several Curves 22
Several waves Several waves Several Curves Interference Pattern 23
What will an electron do? It has mass, so it is matter. A particle can only go through one hole. A wave through both holes. An electron does go through both, and makes an interference pattern. It behaves like a wave. Other matter has wavelengths too short to notice.
Spectrum The range of frequencies present in light. White light has a continuous spectrum. All the colors are possible. A rainbow.
Hydrogen spectrum Emission spectrum because these are the colors it gives off or emits. Called a line spectrum. There are just a few discrete lines showing 434 nm 656 nm 410 nm 486 nm
What this means Only certain energies are allowed for the hydrogen atom. Can only give off certain energies. Use DE = hn = hc / l Energy in the in the atom is quantized.
Niels Bohr Developed the quantum model of the hydrogen atom. He said the atom was like a solar system. The electrons were attracted to the nucleus because of opposite charges. Didn t fall in to the nucleus because it was moving around.
The Bohr Ring Atom He didn t know why but only certain energies were allowed. He called these allowed energies energy levels. Putting Energy into the atom moved the electron away from the nucleus. From ground state to excited state. When it returns to ground state it gives off light of a certain energy.
The Bohr Ring Atom n = 3 n = 4 n = 2 n = 1
Give it some thought As the electron in a hydrogen atom mumps from n=3 orbit to the n=7 orbit, does it absorb energy or emit energy?
The Bohr Model Doesn t work for all atoms. Only works for hydrogen atoms. Electrons don t move in circles. The quantization of energy is right, but not because they are circling like planets.
Limitations to the Bohr Model Bohr model offers an explanation for the line spectrum of the hydrogen atom, it cannot explain the spectra of the other atoms. Important step along the way toward the development of a more comprehensive model 1. Electrons exist only in certain discrete energy levels, described by quantum numbers 2. Energy is involved in moving an electron from one level to another.
The Quantum Mechanical Model A totally new approach. De Broglie said matter could be like a wave. De Broglie said they were like standing waves. The vibrations of a stringed instrument.
What s possible? You can only have a standing wave if you have complete waves. There are only certain allowed waves. In the atom there are certain allowed waves called electrons. 1925 Erwin Schroedinger described the wave function of the electron. Much math but what is important is the solution.
Schroedinger s Equation The wave function is a F(x, y, z) Solutions to the equation are called orbitals. These are not Bohr orbits. Each solution is tied to a certain energy. These are the energy levels.
There is a limit to what we can know German physicist Werner Heisenberg proposed that the dual nature of matter places a fundamental limitation on how precisely we can know both the location and the momentum of any object. The Heisenberg Uncertainty Principle.
Mathematically Dx D(mv) > h/4p Dx is the uncertainty in the position. D(mv) is the uncertainty in the momentum. the minimum uncertainty is h/4p
Examples What is the uncertainty in the position of an electron. mass 9.31 x 10-31 kg with an uncertainty in the speed of.100 m/s What is the uncertainty in the position of a baseball, mass.145 kg with an uncertainty in the speed of.100 m/s
Making sense of it all Because the diameter of a hydrogen atom is only about 1 x 10-10 m, the uncertainty is an order of magnitude greater than the size of the atom. Thus we have essentially no idea where the electron is located within the atom. With the baseball, the uncertainty is so small that it would be inconsequential. M is large and Dx is out of the realm of measurement.
What does Schroedinger s Wave Function mean? nothing. it is not possible to visually map it. The square of the function is the probability of finding an electron near a particular spot. best way to visualize it is by mapping the places where the electron is likely to be found.
Defining the size The nodal surface. The size that encloses 90% to the total electron probability. NOT at a certain distance, but a most likely distance. For the first solution it is a sphere.
S orbitals
P orbitals
P Orbitals
D orbitals
F orbitals
F orbitals
Quantum Numbers There are many solutions to Schroedinger s equation Each solution can be described with 4 quantum numbers that describe some aspect of the solution. 1. Principal quantum number (n) size and energy of an orbital. Has integer values >0
Quantum numbers 2. Angular momentum quantum number l. shape of the orbital. integer values from 0 to n-1 l = 0 is called s l = 1 is called p l =2 is called d l =3 is called f l =4 is called g
Values of l 0 1 2 3 Letter used s Sharp p Princi-pal d Diffuse f Fundamental
Quantum numbers 3. Magnetic quantum number (m l ) integer values between - l and + l, including zero. Describes the orientation of the orbital in space. 4. Electron spin quantum number (m s ) Can have 2 values. either +1/2 or -1/2
Give it some thought What is the difference between an ORBIT in the Bohr model and an ORBITAL in the quantum mechanical model?
Terms Electron shell the collection of orbitals with the same value of n Subshell the set of orbitals that have the same n and l values For example, the orbitals that have n=3, l=2 are called 3d orbitals and are in the 3d subshell.
Electron Configurations Pauli Exclusion Principal no 2 electrons can have the same set of 4 quantum numbers. at most there can only be 2 electrons in a single orbital. Aufbau Principal electrons will fill the lowest energy level first Hund s Rule for orbitals with equal energy, electrons will occupy singly to the maximum extent possible with parallel spin before pairing up.
Increasing energy 7s 6s 5s 4s 3s 2s 7p 6p 5p 4p 3p 2p 6d 5d 4d 3d He with 2 electrons 5f 4f 1s
Fill from the bottom up following the arrows 7s 7p 7d 7f 6s 6p 6d 6f 5s 5p 5d 5f 4s 4p 4d 4f 3s 3p 3d 2s 2p 1s 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2
Details Elements in the same column have the same electron configuration. Put in columns because of similar properties. Similar properties because of electron configuration. Noble gases have filled energy levels. Transition metals are filling the d orbitals
Exceptions Cr = [Ar] 4s 1 3d 5 Half filled orbitals. Scientists aren t sure of why it happens same for Cu [Ar] 4s 1 3d 10
More exceptions Lanthanum La: [Xe] 6s 2 5d 1 Cerium Ce: [Xe] 6s 2 4f 1 5d 1 Promethium Pr: [Xe] 6s 2 4f 3 5d 0 Gadolinium Gd: [Xe] 6s 2 4f 7 5d 1 Lutetium Pr: [Xe] 6s 2 4f 14 5d 1 We ll just pretend that all except Cu and Cr follow the rules.
Writing Electron Configurations Write the electron configuration and orbital diagram for Iron Write the electron configuration and orbital diagram using the short-hand method for Barium.