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Quantum Theory and Atomic Structure. Beyond Bohr (and the others). History – In Brief. 600BC – Thales (Greek) – all matter derived from water. 450BC – Empedocles (Greek) – all matter composed of earth, fire, wind, water
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Quantum Theory and Atomic Structure Beyond Bohr (and the others)
History – In Brief 600BC – Thales (Greek) – all matter derived from water. 450BC – Empedocles (Greek) – all matter composed of earth, fire, wind, water 400BC – Democritus (Greek) – if a substance could be divided into smaller and smaller pieces, eventually it would reach a point where it could not be divided further – ATOM 350BC – Aristotle (Greek) – rejected the atomic model and adopted the 4 element model
History Cont’d 300-1600AD – The Alchemists – 4 element idea – all about the “gold” or Philosopher’s stone – thought to be more perfect than gold, that could be used to bring the base metals up to the perfection of gold. Invented many lab tools, but did not make huge contributions to the nature of matter
John Dalton - 1808 Explained observations of simple compounds by assuming that when two elements combined, the resulting compound contained one of each element. All matter is made up of tiny particles called atoms Atoms of one element are like one another, but different from atoms in other elements Atoms may combine with other atoms to form larger particles called molecules Atoms are neither created nor destroyed by ordinary means
JJ Thomson - 1904 Took an experiment done by William Crookes (cathode ray tube), and noticed that the beam was attracted to the positive charges and repelled by negative charges From this he concluded that an atom must be made up of smaller particles with a negative charge – ELECTRONS Supposed that since most substances are neutral, the atom must be composed of positive particles (later called PROTONS)
Thomson’s Atomic Model Atoms are made of two smaller particles Electrons with a negative charge, and protons with a positive charge The negative charges are embedded in a lump of positive charge
Ernest Rutherford - 1909 Gold Foil Experiment Observations Most of the alpha particles pass straight through the gold foil. Some of the alpha particles get deflected by very small amounts. A very few get deflected greatly. Even fewer get bounced of the foil and back to the left. Rutherford Simulation
Conclusions The atom is 99.99% empty space. The nucleus contains a positive charge and most of the mass of the atom. Electrons orbit the nucleus at very high speeds
Neils Bohr - 1913 Refined Rutherford’s theory to explain why different elements give off different colours when heated Electrons can only exist in certain orbits or shells around the nucleus. Each shell has a unique distance from the nucleus and can only hold a fixed number of electrons
Visible light is a type of electromagnetic radiation. • Other types include x-rays, microwaves, and radio waves. • The classical wave model distinguishes between waves and particles, but cannot explain atomic scale observations.
Frequency - , represents the number of cycles the wave undergoes per second (units of 1/s or Hz) • Wavelength - , is the distance between any point on a wave and the corresponding point on the next wave (units – nm, 10-9m) • In a vacuum, all types of electromagnetic radiation travel at 3.00x108m/s (c)
Electromagnetic Spectrum http://kirkwoodschools.org/faculty/mcgeech/upload/4845f11eadc9a.jpg
Calculating Frequency • The yellow light given off by a sodium vapor lamp used for public lighting has a wavelength of 589nm. What is the frequency of this radiation?
Practice: • A laser used in eye surgery to fuse detached retinas produces radiation with a wavelength of 640.0nm. Calculate the frequency of this radiation. • An FM radio station broadcasts electromagnetic radiation at a frequency of 103.4MHz. Calculate the wavelength of this radiation. Worksheet
When solids are heated, they emit radiation. • In 1900, Max Planck assumed that energy can be either released or absorbed by atoms only in discrete “chunks” of some minimum size. • Called the smallest quantity of energy that can be emitted or absorbed as electromagnetic radiation a QUANTUM. h=6.62x10-34Js
Calculating Energy of a Photon • Calculate the energy of one photon of yellow light with a wavelength of 589nm.
Practice • A laser emits light with a frequency of 4.69x1014Hz. What is the energy of one photon of the radiation from this laser? • If the laser emits 1.3x10-2J during a pulse, calculate the wavelength of the laser. Worksheet
Line Spectra • In 1913, Niels Bohr offered a theoretical explanation of line spectra. • Try my “goggles” • A spectrum is produced when radiation from sources like stars and light bulbs are separated into its different wavelength components. LAB – Atomic Emission Spectra
Line Spectra Cont’d • The line spectra of hydrogen was among the first to be widely studied. • There are only 4 lines in the hydrogen spectra. • In 1885, Johann Balmer showed that the wavelengths of the four visible lines fit a simple formula. http://www.etresoi.ch/Denis/img/HydrogenSpectra.jpg RH = -2.179x10-18J ni and nf are positive integers Periodic Table of Spectra
Bohr’s Model • To explain the line spectra of hydrogen, Bohr assumed that electrons move in circular orbits around the nucleus. • If so, as the electron lost energy it should CRASH into the nucleus (which it doesn’t) since hydrogen atoms are stable. • Bohr adopted Planck’s idea that energies are quantized (big no no?).
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.
Practice • Predict which of the following electronic transitions produces the spectral line having the longest wavelength: n=2 to n=1, n=3 to n=2, or n=4 to n=3. Answer: The wavelength increases as frequency decreases (=c/). So, the longest wavelength will be associated with the lowest frequency. According to Planck’s equation (E=h), the lowest frequency is associated with the lowest energy. The shortest vertical line (see previous slide image) represents the smallest energy change. Thus the n=4 to n=3 transition produces the longest wavelength (lowest frequency) line.
Poor Bohr (Limitations) • Bohr model explains hydrogen very well, but the model is unable to explain the spectra of other elements. • Bohr also avoided the problem of why the electron would not fall into the nucleus. • Great “first” step, but much more to come! • But what’s good about Bohr model: • Electrons exist in discrete energy levels, described by quantum numbers. • Energy is involved in moving an electron from one level to another.
De Broglie suggested that as the electron moves about the nucleus, it is associated with a particular wavelength. De Broglie used the term MATTER WAVES to describe the wave characteristics of material particles. mv quantity is called its MOMENTUM
Uncertainty Principle • Heisenberg’s uncertainty principle states that it is impossible to know the exact momentum of the electron and its exact location in space. http://www.ostheimer.at/mambo/images/stories/Werner_Heisenberg_Tafel.jpg
Schrödinger • In 1962 proposed an equation that incorporated both the wavelike behaviour and the particle-like behaviour of the electron. • This new “way” of thinking was dubbed quantum mechanics or wave mechanics. • Uses the symbol is Ψ2 (probability density/electron density)
Orbitals and Quantum Numbers • Schrodinger’s equation yields a set of wave functions and corresponding energies called orbitals, each orbital has corresponding quantum numbers.
The collection of orbitals with the same value of n is called an electron shell. • The set of orbitals that have the same n and l values is called a subshell. • The total number of orbitals in a shell is n2
The s-orbitals • S-orbitals are spherical (symmetric) • S-orbitals have an angular momentum quantum number of l=0 and ml=0. • S-orbitals can only contain 2 electrons.
The p-orbitals • Electron density of this orbital in concentrated in two regions on either side of the nucleus. • P-orbitals have l=1, their ml=-1,0,1 • Orbitals contain up to 6 electrons in 3 subshells.
The d and forbitals • d-orbitals occur at n=3, l=2, and have 5 different orbitals (10 electrons) • f-orbitals occur at n=4, l=3, and have 7 different orbitals (14 electrons).
Many-Electron Atoms Okay – now what? I’m already overwhelmed!
Orbitals and Their Energies • The quantum theory allows scientists to explain the electronic structure of atoms that have more than 2 electrons (ie. like hydrogen) • Though orbitals can have the same n value (energy level), their energies can vary due to electron-electron repulsions. • For example: 3s < 3p < 3d – the 3d orbital is slightly higher in energy than the 3p or 3s orbital
Electron Spin and the Pauli Exclusion Principle • In 1925, Uhlenbeck and Goudsmit discovered why some line spectra seemingly had 2 lines – electron spin. • Electron spin causes each electron to behave as if it were a tiny sphere spinning on its own axis.
Electron spin is quantized! • Its is called the spin magnetic quantum number, ms • ms = + ½ or -½ • Also in 1925, Wolfgang Pauli discovered that no two electrons in an atom can have the same set of four quantum numbers – n, l, ml, ms (this was called the PAULI EXCLUSION PRINCIPLE) • ∴ We can conclude that each orbital can hold a maximum of 2 electrons which must have different spins.
