Atomic Physics -2
Atomic Spectra Fill a glass tube with pure atomic gas Apply a high voltage between electrodes Current flows through gas & tube glows Color depends on type of gas Light emitted is composed of only certain wavelengths
Atomic Spectra Emission Spectrum: diagram or graph that indicates the wavelengths of radiant energy that a substance emits (bright lines) Absorption Spectrum: same thing, just for light absorbed by a substance (dark lines) What does this have to do with atomic models?
Energy Levels & Emission Spectra Lowest energy state: ground state Radius of this state: Bohr radius Electrons usually here at ordinary temps How do electrons jump between states? Absorb photon with energy (hf) exactly equal to energy difference between ground state & excited state Absorbed photons account for dark lines in absorption spectrum
Energy Levels & Emission Spectra Spontaneous emission: Electron in excited state jumps back to a lower energy level by emitting a photon Does NOT need to jump all the way back to the ground state Emitted photon has energy equal to energy difference between levels Accounts for bright lines on emission spectrum Jumps between different energy levels correspond to various spectral lines
Photon Energy The equation for determining the energy of the emitted photon in any series: E = 1 1 13.6 ev 2 n 2 f n i
Balmer Wavelengths
The Balmer Series In the Balmer Series n f = 2 There are four prominent wavelengths 656.3 nm (red) 486.1 nm (green) 434.1 nm (purple) 410.2 nm (deep violet)
The Balmer Series Wavelength Equation R H is the Rydberg constant 1 λ = R H R H = 1.0973732 x 10 7 m -1 1 2 2 1 n 2 i
Two Other Important Series Lyman series (UV) n f = 1 Paschen series (IR) n f = 3
Different Elements = Different Emission Lines
Emission Line Spectra So basically you could look at light from any element of which the electrons emit photons. If you look at the light with a diffraction grating the lines will appear as sharp spectral lines occurring at specific energies and specific wavelengths. This phenomenon allows us to analyze the atmosphere of planets or galaxies simply by looking at the light being emitted from them.
The Absorption Spectrum An element can absorb the same wavelengths that it emits. The spectrum consists of a series of dark lines.
Energy levels Application: Spectroscopy Spectroscopy is an optical technique by which we can IDENTIFY a material based on its emission spectrum. It is heavily used in Astronomy and Remote Sensing. There are too many subcategories to mention here but the one you are probably the most familiar with are flame tests. When an electron gets excited inside a SPECIFIC ELEMENT, the electron releases a photon. This photon s wavelength corresponds to the energy level jump and can be used to indentify the element.
Identifying Elements The absorption spectrum was used to identify elements in the solar atmosphere. Helium was discovered.
Thermal vs. Atomic Spectra How could you tell if the light from a candle flame is thermal or atomic in origin?
If the spectrum is continuous, the source must be thermal.
Three Types of Spectra
Three Types of Spectra (continued)
Three Types of Spectra (continued)
Quantum Numbers Set of 4 numbers which identify an electron. Principal quantum number n 1-7 sublevel quantum number l spdf orientation quantum number m spin quantum number s + -
Four Quantum Numbers The state of an electron is specified by four quantum numbers. These numbers describe all possible electron states. The total number of electrons in a particular energy level is given by: # = 2n 2
Principle Quantum Number The principal quantum number (n) where n = 1, 2, 3, Determines the energy of the allowed states of hydrogen States with the same principal quantum number are said to form a shell K, L, M, (n = 1, 2, 3, )
Orbital Quantum Number The orbital quantum number (l) where l ranges from 0 to (n 1) in integral steps Allows multiple orbits within the same energy level Determines the shape of the orbits States with given values of n and l are called subshells s (l = 0), p (l = 1), d (l = 2), f (l = 3), etc
Electron Subshells
Generally, the electrons in the s subshell are at the lowest energy level and those in the f subshell in the highest shell occupy the highest energy level.
As the shell number (n) increases the energy difference between the shells diminishes, as shown by the decreasing distance between each successive shell.
Electron Subshells
Magnetic Quantum Number The magnetic quantum number (m l ) where m l ranges from - l to + l in integral steps Explains why strong magnetic fields can cause single spectral lines to split into several closely spaced lines Called the Zeeman effect
Spin Magnetic Quantum Number The spin magnetic quantum number (m s ) where m s can only be + 0.5 or 0.5 Accounts for the fine structure of single spectral lines in the absence of a magnetic field
Quantum Mechanics And The Hydrogen Atom A review of the various quantum number ranges which are used to determine allowable states n can range from 1 to infinity in integral steps l can range from 0 to (n - 1) in integral steps m l can range from l to + l in integral steps m s can only be + ½ or ½
Orbitals Each orbital has its own set of quantum numbers. Each orbital can contain 2 electrons, one with spin +1/2 the other with spin -1/2 The quantum number and energy levels can be described with an orbital diagram. A summary of an orbital diagram is called an electron configuration.
Energies of Orbitals in Multi- Electron Atoms Several factors affect the energy of electrons in multi electron atoms: Nuclear charge Electron repulsions Additional electrons in the same orbital (shielding) Additional electrons in inner orbitals Orbital shape (m l ) spin (m s ) Pauli Exclusion Principle: No two electrons in the same atom can have the same set of four quantum numbers.
Hund s Rule Electrons enter orbitals one at a time before becoming paired.
Aufbau Principle Placement of electrons occur in the lowest energy levels of orbitals first then into higher levels They go into the orbitals one with spin +1/2, the other with spin - 1/2. An orbital diagram is useful in showing this arrangement.
Orbital Diagrams
Electronic Configurations By adding electrons to the diagram, lowest energy to highest, remembering Hund s rule and the quantum rule that no orbital can hold more than two electrons, an elcetronic configuration can be created
The Octet Rule The maximum number of electrons in the outer energy level of an atom is 8. Atoms form compounds to reach eight electrons in their outer energy level. Atoms with less than 4 electrons in their outer level tend to lose electrons to form compounds. Atoms with more than 4 electrons in their outer level tend to gain electrons to form compounds.
Electron Configurations can be Determined From the Position in the Periodic Table: Elements in group 1(1A) end in ns 1. Elements in group 2 (2A): end in ns 2 Elements in group 13 (3A) end in ns 2 np 1 Elements in group 14 (4A): end in ns 2 np 2 Elements in group 15 (5A) end in ns 2 np 3 Elements in group 16 (6A) end in ns 2 np 4 Elements in group 17 (7A) end in ns 2 np 5 Elements in group 18 (8A) end in ns 2 np 6
Periodic Table Family Filling Diagram
The Pauli Exclusion Principle Two electrons in an atom can never have the same set of 4 quantum numbers. Because of this, the elements all have different chemical properties. The n = 1 energy level is filled with electrons first.
The Pauli Exclusion Principle And The Periodic Table Mendeleev arranged the elements in a periodic table according to their atomic masses and chemical similarities. He left gaps which were filled in within the next 20 years. Vertical columns have similar chemical properties.
The Periodic Table
Hydrogen Like Atoms Two important equations for hydrogen-like atoms: Orbital energy Orbital radius Z 2 E n = 2 ( 13.6) ) ev n r n = (0.0529 nm) n2 Z
Wave Properties It became generally agreed upon that wave properties were involved in the behavior of atomic systems.
Bohr s Model was improved upon in the 1920 s with the Quantum Mechanical Model. Since Bohr s model only worked for the hydrogen atom, a more sophisticated model was needed. The next breakthrough was made by Louis de Broglie, who suggested that electrons, like photons have wave properties De Broglie thought that Bohr s energy levels were created by the wave properties of the electron
Matter Waves Louis de Broglie (1924) suggested that if waves can behave like particles, maybe particles can behave like waves. He proposed that electrons are waves of matter. The reason for the size and number of electrons in a Bohr electron shell is the number of wave periods that exactly fit.
Schrödinger s Wave Equations In 1926, Erwin Schrödinger published a general theory of matter waves. Schrödinger s equations describe 3-dimensional waves using probability functions Gives the probability of an electron being in a given place at a given time, instead of being in an orbit The probability space is the electron cloud.
Heisenberg s Uncertainty Principle Werner Heisenberg German physicist, 1901-1976 Schrödinger s equations give the probability of an electron being in a certain place and having a certain momentum. Heisenberg wished to be able to determine precisely what the position and momentum were.
Heisenberg s Uncertainty Principle It is impossible to know a particles exact position and velocity simultaneously. The act of observing alters the reality being observed. There is a limit on measurement accuracy that is significant but of practical importance when dealing with particles of atomic and subatomic size
Heisenberg s Uncertainty Principle, 2 To see an electron and determine its position it has to be hit with a photon having more energy than the electron which would knock it out of position. To determine momentum, a photon of low energy could be used, but this would give only a vague idea of position. Note: the act of observing alters the thing observed.
Heisenberg s Uncertainty Principle, 3 Using any means we know to determine position and momentum, the uncertainty of position, q, and the uncertainty of momentum, p, are trade-offs. q p h/2π, where h is Planck s constant
Particles or Waves? Question: Are the fundamental constituents of the universe Particles which have a position and momentum, but we just can t know it, or Waves (of probability) which do not completely determine the future, only make some outcome more likely than others?
Evidence for Matter Waves 1927: Davisson & Germer, showed that electrons can be diffracted by a single crystal of nickel Electron diffraction is possible because the de Broglie wavelength of an electron is approx. equal to distance between atoms (the size of the diffraction grating) Large-scale objects don t demonstrate this well because large momentum generates wavelengths much smaller than any possible aperture through which the object could pass (won t be diffracted)
The Copenhagen Interpretation Niels Bohr and Werner Heisenberg: The underlying reality is more complex than either waves or particles. We can think of nature in terms of either waves or particles when it is convenient to do so. The two views complement each other. Neither is complete in itself and a complete description of nature is unavailable to us. Heisenberg & Bohr
The Copenhagen Interpretation Niels Bohr and Werner Heisenberg: The underlying reality is more complex than either waves or particles. We can think of nature in terms of either waves or particles when it is convenient to do so. The two views complement each other. Neither is complete in itself and a complete description of nature is unavailable to us. Heisenberg & Bohr
Evolving Theories of the Atom
Electromagnetic Radiation Before we can explore our model of the atom further, we need to look more closely at energy Chemistry is the study of matter and energy. One type of energy is electromagnetic radiation. Let us look more closely at the properties of electromagnetic waves. Electromagnetic waves consist of oscillating, perpendicular electric and magnetic fields. The wavelength of radiation is the distance between peaks in a wave. (λ) The frequency is the number of peaks that pass a point in a second. (ν )
Wavelength of Light
A Simple Frequency and Wavelength Formula λν = c λ = c/ν ν = c/λ λ is wavelength measured in length units (m, cm, nm, etc.) ν is frequency measured in Hz (s -1 ). c is the velocity of light in vacuum = 3.0 x10 8 ms -1
Electromagnetic Spectrum Recognize common units for λ, ν. λ wavelength ν frequency meters (m) radio Hertz Hz s -1 micrometers υm (cycles per (10-6 m) microwaves second) nanometers nm megahertz (10-9 m) light MHz (10 6 Hz) A angstrom (10-10 m)
Electromagnetic Waves Describe electromagnetic radiation and give examples of it in relation to the electromagnetic spectrum. Type λ (nm) ν (Hz) radio (Rf) 10 8-10 12 10 4-10 9 microwave 10 6-10 8 10 9-10 12 infrared (IR) 750-10 6 10 12-10 14 visible (vis) 400-750 10 14-10 15 ultraviolet (UV) 10-400 10 15-10 16 X-rays, γ rays 10-4 -1 10 16-10 22
The Electromagnetic Spectrum
Light Quanta and Photons Quantum- A packet of energy equal to hν. The smallest quantity of energy that can be emitted or absorbed. Photon- A quantum of electromagnetic radiation. Thus light can be described as a particle (photon) or as a wave with wavelength and frequency. This is called wave-particle duality (one of the most profound mysteries of science)
Emission Lines
Modern Atomic Theory All matter is composed of atoms. Atoms of the same element are chemically alike with a characteristic average mass which is unique to that element. Atoms cannot be subdivided, created, or destroyed in ordinary chemical reactions. However, these changes CAN occur in nuclear reactions! Atoms of any one element differ in properties from atoms of another element The exact path of electrons are unknown and e - s are found in the electron cloud.
The Atomic Scale Most of the mass of the atom is in the nucleus (protons and neutrons) Electrons are found outside of the nucleus (the electron cloud) Most of the volume of the atom is empty space q is a particle called a quark
Albert Einstein 1879-1955 He published 5 papers in 1905. Photoelectric effect using Planck s ideas of quanta of energy won Nobel prize E=mc 2 became the basis of the atomic bomb.
Albert Einstein Used Planck s hypothesis to describe light in terms of particles rather than waves photoelectric effect-electrons are emitted when certain metallic materials are exposed to light Photons-packets of energy E=hf f= c/wavelength the shorter the wavelength =more energy
Dual nature of light Light acts sometimes like a wave and sometimes like a particle Wavelength of light must have enough energy to free electrons Photon=particle of energy atoms absorb quanta of energy and emit electrons
Max Planck German 1900 s 1. Quantum Physics 2. Planck s hypothesisenergy was quantized or oscillators could have only discrete or certain amount of energy and depends on its frequency E=hf h=6.63 x 10-34
Max Planck is famous for proposing a quantum hypothesis for light The energy of a light quantum has been found to be directly proportional to the frequency of the light.
Quantum A discrete amount of energy emitted or absorbed electromagnetic waves 3x 10 8 m/s quanta-bundles of energy
Blackbody Radiation One of the earliest indications that classical physics was incomplete came from attempts to describe blackbody radiation. A blackbody is an ideal surface that absorbs all incident radiation. Blackbody radiation is the emission of electromagnetic waves from the surface of an object. The distribution of blackbody radiation depends only the temperature of the object.
The Blackbody Distribution The intensity spectrum emitted from a blackbody has a characteristic shape. The maximum of the intensity is found to occur at a wavelength given by Wien s Displacement Law: f peak = (5.88 10 10 s -1 K -1 )T T = temperature of blackbody (K)
The Ultraviolet Catastrophe Classical physics can describe the shape of the blackbody spectrum only at long wavelengths. At short wavelengths there is complete disagreement. This disagreement between observations and the classical theory is known as the ultraviolet catastrophe.
Planck s Solution In 1900, Max Planck was able to explain the observed blackbody spectrum by assuming that it originated from oscillators on the surface of the object and that the energies associated with the oscillators were discrete or quantized: E n = nhf n = 0, 1, 2, 3 n is an integer called the quantum number h is Planck s constant: 6.62 10-34 J s f is the frequency
Quantization of Light Einstein proposed that light itself comes in chunks of energy, called photons. Light is a wave, but also a particle. The energy of one photon is E = hf where f is the frequency of the light and h is Planck s constant. Useful energy unit: 1 ev = 1.6 10-19 J
Quantum Mechanics The essence of quantum mechanics is that certain physical properties of a system (like the energy) are not allowed to be just any value, but instead must be only certain discrete values.
The PhotoElectric Effect When light is incident on a surface (usually a metal), electrons can be ejected. This is known as the photoelectric effect. Around the turn of the century, observations of the photoelectric effect were in disagreement with the predictions of classical wave theory.
Observations of the Photoelectric Effect No electrons are emitted if the frequency of the incident photons is below some cutoff value, independent of intensity. The maximum kinetic energy of the emitted electrons does not depend on the light intensity. The maximum kinetic energy of the emitted electrons does depend on the photon frequency. Electrons are emitted almost instantaneously from the surface.
The Photoelectric Effect Explained (Einstein 1905, Nobel Prize 1921) The photoelectric effect can be understood as follows: Electrons are emitted by absorbing a single photon. A certain amount of energy, called the work function, W 0, is required to remove the electron from the material. The maximum observed kinetic energy is the difference between the photon energy and the work function. K max = E W 0 E = photon energy
The Mass and Momentum of a Photon Photons have momentum, but no mass. We cannot use the formula p = mv to find the momentum of the photon. Instead: hf p = = c h λ
The Wave Nature of Particles We have seen that light is described sometimes as a wave and sometimes as a particle. In 1924, Louis debroglie proposed that particles also display this dual nature and can be described by waves too! The debroglie wavelength of a particle is related to its momentum: λ= h/p
Wave Model
The Wave Model Today s atomic model is based on the principles of wave mechanics. According to the theory of wave mechanics, electrons do not move about an atom in a definite path, like the planets around the sun.
The Wave Model In fact, it is impossible to determine the exact location of an electron. The probable location of an electron is based on how much energy the electron has. According to the modern atomic model, an atom has a small positively charged nucleus surrounded by a large region (a cloud) in which there are enough electrons to make an atom neutral.
Electron Cloud: Depending on their energy they are locked into a certain area in the cloud. Electrons with the lowest energy are found in the energy level closest to the nucleus Electrons with the highest energy are found in the outermost energy levels, farther from the nucleus This model explains spectral lines of an atom. Quantum model of the atom
e e e + e + e + + + e e + e + e + e Thomson s plum-pudding model (1897) - - - + - - Rutherford s model (1909) Bohr s model (1913) Charge-cloud model (present) 1803 John Dalton pictures atoms as tiny, indestructible particles, with no internal structure. 1897 J.J. Thomson, a British scientist, discovers the electron, leading to his "plum-pudding" model. He pictures electrons embedded in a sphere of positive electric charge. 1911 New Zealander Ernest Rutherford states that an atom has a dense, positively charged nucleus. Electrons move randomly in the space around the nucleus. 1913 In Niels Bohr's model, the electrons move in spherical orbits at fixed distances from the nucleus. 1926 Erwin Schrodinger develops mathematical equations to describe the motion of electrons in atoms. His work leads to the electron cloud model. 1904 Hantaro Nagaoka, a Japanese physicist, suggests that an atom has a central nucleus. Electrons move in orbits like the rings around Saturn. 1924 Frenchman Louis de Broglie proposes that moving particles like electrons have some properties of waves. Within a few years evidence is collected to support his idea. 1932 James Chadwick, a British physicist, confirms the existence of neutrons, which have no charge. Atomic nuclei contain neutrons and positively charged protons.
Greek Dalton Thomson Indivisible Electron Nucleus Orbit Electron Cloud X X X Rutherford X X Bohr X X X Wave X X X
shorthand Atomic number Z = number of protons Mass number A = mass of nucleons a z 35 17 12 6 x Cl C
Radioactive Isotopes and radioactivity Radioisotopes - isotopes that have unstable nuclei and will spontaneously disintegrate and emit radiation. Becquerel 1896 mineral pitchblende Curie 1898 radium and polonium Three types or radiation: 1. Alpha particles 2. Beta particles 3. Gamma radiation
Isotopes Isotopes are atoms of the same element with different numbers of neutrons C 12 C 13 C 14 Atoms which give out radioactivity are called radioactive isotopes. The nucleus of a radioactive isotope is unstable.
Einstein Energy/Mass Equivalence In 1905, Albert Einstein publishes a 2 nd major theory called the Energy-Mass Equivalence in a paper called, Does the inertia of a body depend on its energy content?
Energy Unit Check 2 2 2 2 2 2 2 s m kg m s m kg W E s m kg N ma F Nm Joule Fx W s m kg Joule mc E net B = = = = = = = = =
Mass Defect The nucleus of the atom is held together by a STRONG NUCLEAR FORCE. The more stable the nucleus, the more energy needed to break it apart. Energy need to break the nucleus into protons and neutrons is called the Binding Energy Einstein discovered that the mass of the separated particles is greater than the mass of the intact stable nucleus to begin with. This difference in mass ( m) is called the mass defect.
Mass Defect - Explained The extra mass turns into energy holding the atom together.
Mass Defect Example