Atomic Structure Chapter 7: Describe the properties of electromagnetic radiation. Understand the origin of light from excited atoms and its relationship to atomic structure. Describe the experimental evidence for wave-particle duality. Describe the basic ideas of quantum mechanics. Define the three quantum numbers and their relationship to atomic structure.
Electromagnetic Radiation • Radiation is _____________! • List forms of electromagnetic radiation: _______________ ___________ _______________ ___________ • Maxwell Theory (1831-1879): describe all forms of radiation in terms of ________ ________________________________. • Einstein Theory (1879-1955): light has _______________________________.
Wave Properties wavelength Visible light Ultraviolet radiation
Electromagnetic Radiation Frequency – hertz (s-1) Speed = wavelength (m) x frequency (s-1) c = l x v
What is the frequency of orange light, which has a wavelength of 625 nm? Students should be familiar with conversion of units and conversion between l and v.
The Visible Spectrum of Light • Long wavelength --> ______ frequency _____ energy • Short wavelength --> _____ frequency _____ energy
Energy and Frequency • Max Planck (1858-1947): the energy of a vibrating systems is proportional to the frequency of vibration. • The proportionality constant h = Planck’s constant = 6.6260693 x 10-34 J s E = h v
Radiation given off by a Heated Body • Planck solved the “___________________”. • Vibrations are _________ – only vibrations with specific frequencies are allowed. • There is a distribution of vibrations in a object.
Quantization of Energy • An object can gain or lose energy by absorbing or emitting radiant energy in QUANTA. • Energy of radiation is proportional to frequency. Light with large l (small v) has a _____ E. Light with a short l (large v) has a ____ E. E = h v
Photoelectric Effect • Experiment demonstrates the _______ _____________________________. No e- observed until light of a certain minimum E is used.
Photoelectric Effect • Classical theory said that E of ejected electron should increase with increase in light frequency—not observed! • No e- observed until light of a certain minimum E is used. • If the frequency is above the minimum, the number of e- ejected depends on light intensity. • Einstein explained the photoelectric effect: light consists of “__________” particles called PHOTONS – _______________. • The energy of each photon is proportional to the ______________of radiation (Planck’s relation). • The greater the intensity of light, the more photons are available to strike per unit of time.
Show that the energy of a mol of blue photons (l = 400 nm) is higher than the energy of a mol of red photons (l=685 nm)
~ = h c v Using Planck’s Equation • As frequency (v) increases, energy (E) __________. • As wavelength (l) decreases, energy (E) _________. E = h v v = c/l E = h v = h c l (wavenumber) Students should be familiar with frequency, wavelength, and energy calculations.
Photosynthesis • Chlorophylls absorb blue and red light and carotenoids absorb blue-green light, but green and yellow light are not effectively absorbed by photosynthetic pigments in plants; therefore, light of these colors is either reflected by leaves or passes through the leaves. This is why plants are green.
Spectrum of Excited Hydrogen Gas • Excited atoms emit light of only certain wavelengths. –Evidence of ____________________. • Line Emission Spectra of Excited Atoms. • The wavelengths of emitted light depend on ______________________________.
1 l 1 22 1 n2 ( ) = R Which Mathematical Expression represents the Regular Patterns of Emission? • Johann Balmer (1825-1898) and Johannes Rydberg (1854-1919) developed an equation: • Rydberg equation – to calculate the _________________ __________________ __________________. • Rydberg constant = R R = 1.0974 x 107 m-1 when n > 2 n = 3 , l =red line n = 4 , l = green line, Etc. Balmer Series
Atomic View of the Early 20th Century An electron (e-) traveled about the nucleus in an orbit. 1. Any orbit should be possible and so is any energy. 2. But a charged particle moving in an electric field should emit energy. End result should be matter self-destruction!
Bohr Model • Niels Bohr (1885-1962) connected the observation of the spectra of excited atoms with the quantum ideas of Planck and Einstein. • Based on Rutherford’s work – electrons are arranged in space outside the atom. • Bohr model shows electrons moving in a circular orbit around the nucleus. • Bohr postulated: 1.- An electron could occupy only __________ ___________or energy levels in which it is stable. 2.-The energy of the electron in the atom is ______________.
Atomic Spectra and Bohr • n ___________ quantum number • n is a _________________ having values of 1, 2, 3 and so on. • The energy of attraction between oppositely charged bodies (negative electron and positive nuclear proton) has a negative value. The value becomes more negative as the bodies move closer together (Coulomb’s law). • As the value of n increases, the energy becomes less negative, the distance of the electron from the nucleus increases. Rh c n 2 Potential energy of electron in the nth level = En = -
n = 2 2 E = -C (1/ 2 ) n = 1 2 E = -C (1/1 ) Atomic Spectra and Bohr • Only orbits where n = integral number are permitted. If e-’s are in quantized energy states, then ∆E of states can have only certain values. This explain sharp line spectra.
Ground State and Excited State • Ground state: The state of an atom in which all electrons are in the ______________________. • Excited state: The state of an atom in which at least one electron is ______________________ ____________________.
CC alculateDE for an e- of the H atom “falling” from high energy level (n = 2) to low energy level (n = 1).
Atomic Spectra and Bohr • The amount of energy that must be absorbed by the atom so that an electron can move from the first to the second energy state is 3/4RhC or 984 kJ/mol of atoms – no more or less – energy levels in the H atom are quantized – only certain amounts of energy may be absorbed or emitted. • When an electron “falls” from a level of higher n to one of lower n, ________ energy. The negative sign indicates energy is _________, 984 kJ must be _______ per mole of H atoms. • The energy ________ is observed as ______ – This is the source of the lines observed in the emission spectrum of H atoms. – The basic explanation holds for the spectra of other elements.
Atomic Spectra and Bohr 1 1 • The origin of atomic spectra is the movement of _________ between quantized energy states. • Electron is excited from a lower energy state to a higher one – Energy is ________. • Electron moves from a higher energy state to a lower one – Energy is _________. ( ) - ∆E = Efinal – Einitial = -R h c n2final n2initial
Electronic Transitions in an Excited H Atom • If electrons move from energy states n >1 to the n =1 state – emission lines have energies in the UV region (Lyman series). • If electrons move from energy states n >2 to the n =2 state – emission lines have energies in the VIS region (Balmer series). • If electrons move from energy states n >3 to the n =3 state – emission lines have energies in the IR region.
Calculate the wavelength of the photon emitted if an electron in the H atom moves from n = 4 to n =2
Flaws in Bohr’s Theory • Bohr’s model of the atom explained only the spectrum of H atoms and of other systems having one electron (such as He+). • The idea that electrons are particles moving about the nucleus with a path of fixed radius, like that of the planets about the sun, is no longer valid.
Wave Mechanics Louis de Broglie (1892-1987) proposed that all moving objects have _______ _________________(1924). For light: (1) E = mc2 (2) E = h v = h c / l
Wave Mechanics –Calculate the Broglie Wavelength Baseball (115 g) at 100 mph e- with velocity = 1.9 x 108 cm/sec It is possible to observe wave-like properties only for particles of extremely __________, such as protons, neutrons, and electrons. l= h m v
The Uncertainty Principle • Erwin Schrödinger, 1887-1961 : developed ________________or ______________. • Werner Heisenberg, 1901-1976 : The uncertainty principle – it is impossible to fix both the ______________ electron in an atom and its ________ with any degree of certainty. • Max Born, 1882-1970 : if the energy of an electron in an atom is known with a small uncertainty, there will be large uncertainty in its position in the space about the atom's nucleus. • We can assess only the likelihood, or probability, of finding an electron with a given energy within a given region of space.
Schrödinger's Wave Functions • The behavior of the electron in the atom is best described as a standing wave – In a vibrating string, only certain vibrations can be observed = only certain wave functions are allowed for the electron in the atom. • Each wave function () is associated with an allowed energy value, En, for the electron. • Then, from 1 and 2, the energy of the electron is quantized – only certain values of energy. Wave motion:wave length and nodes 4. In contrast to Bohr’s theory – quantization is imposed as a postulate.
Schrödinger's Wave Functions 5. The is related to the probability of finding the electron within a given region of space = _______________. 6. Energy is known precisely – position is given by a probability. The region of space in which an electron of a given energy is most probably located is called its _______________. 7. The solution to the Schrödinger's equation, for an electron, in a 3-D space, are 3 integer numbers = quantum numbers n, l, and ml. These numbers have only certain combination of values.
Quantum numbers • n, Principal quantum number = 1, 2, 3, … Determines the ________ of the electron. Also related to size of orbital. En = - Z2h R / n2 Electrons with the same n value are in the same electron ______ or same electron _________. • l, Angular Momentum quantum number = 0, 1, 2, 3, …, n-1 Determines the ______ at which electrons circulate about the nucleus. Related to orbital __________. Electrons with the same l value are in the same _______ and have the same orbital _____ (______). All orbitals in the same subshell have the same ___________. • ml, Magnetic quantum number = 0, ±1, ± 2, ± 3, …, ±l Determines the _____________ of the orbital motion of the electron. (Clockwise or counterclockwise). Related to ___________ in space of the orbitals within a subshell, this gives the ___________ of orbitals in a subshell. See Table 7.1 (p 319)
Quantum numbers and Orbitals Number of subshells in a shell = n Number of orbitals in a subshell = 2l + 1 Number of orbitals in a shell = n2 l =0 (s) ; l =1 (p) ; l =2 (d) ; l =3 (f) Name of orbital = value of n and letter code for l If n=1 ; l = n-1 = 0 ; ml = 0 Only 1 subshell (s); only 1 orbital (1s) If n=2 ; l = 0, 1 ; ml = +1, 0, -1 There are 2 subshells (s and p) 4 orbitals (the 2s, and three 2p (3 orientations)
Orbitals • Electron orbitals are probabilities – represented as ____________________.
Orbitals surface density plot or radial distribution plot • For the s orbital, the probability of finding an electron is the same at the same distance from the nucleus – the 1s orbital is ____________ in shape. • Quantum mechanics – electron has wave properties – the maximum amplitude of the electron wave occurs at 0.053 nm from the nucleus. • Bohr’s radius = 0.059 nm
Orbitals • The p orbitals have 1 nodal surface – zero probability of finding an electron. • Number of nodal surfaces = value of l • There are three p orbitals in each p subshell: ml = +1, 0, -1 • Refer to orbitals according to the axes along which the lobes lie: px, py, pz
Orbitals • The d five orbitals, l=2 have 2 nodal surfaces (may not be flat). • What type of orbital is designated n = 4, l = 3, ml =-3? a. 4s b. 4p c. 4d d. 4f e. none
Orbitals Students should be familiar with definitions of quantum numbers and orbital types.
Practice • Which of the following represent valid sets of quantum numbers? • n=3, l=3, ml= +1 • n=5, l=1 • n=6, l=5, ml=1 • n=4, l=3, ml=-4
Remember • Go over all the contents of your textbook. • Practice with examples and with problems at the end of the chapter. • Practice with OWL tutors. • W ork on your assignment for Chapter 7. • Practice with the quiz on the cd or online service.