Chapter 7: Quantum Theory & Atomic Structure
Chapter 7: Quantum Theory & Atomic Structure CH 121
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Date Created: 12/01/15
Chapter 7 Lecture Notes Chemical bonding o Electron orbitals Electron magnetic radiation o Most subatomic particles behave as particles and obey physics of waves EM radiation curves o Wavelength (lambda) - distance from peak to peak o Frequency (nu) - number of cycles per unit time o Amplitude- height from starting point to wave peak EM radiation o Consists of an oscillating electric and magnetic field o Waves have a frequency o Use nu for frequency = lambda x nu = c Wavelength (frequency): constant, speed of light C= velocity of light: 3.00 x 10^8 m/s o Long wavelength --> smaller frequency o Short wavelength --> higher frequency EM spectrum o Long wavelength --> low frequency, low energy o Short wavelength --> high frequency, high energy o Red light lambda = 700 nm --> calculate frequency Nano = 10^-9 m Lambda x nu = c 700nm 10^-9 m 1 nm = 7.00 x 10^-7 m Nu = c/lambda 3.00x10^8 m/s 7.00 x 10^- 7 m = 4.29 x 10^4 sec^-1 Quantization of energy o Wave model of light can explain some behavior, but not all (early 1900's) o Heated objects emit light (blackbody radiation) o Emission of electrons from metal surfaces on which light shines (photoelectric effect) o Emission of light from electronically excited gas atoms (emission spectra) o Max Planck solved by quantization - theory that energy is absorbed or released by atoms in discrete "chunks" o Only certain wavelength allowed o An object can gain or lose energy in quanta o Energy of red is proportional to frequency E = h x v H= 6.626 x 10^-34 J(s) o Matter is allowed to emit and absorb energy in only whole number multiples of hu (3 hu = 3 quanta) o Light with large lambda (small nu) has small E o Light with short lambda (large nu) has high E Photoelectric effect o Demonstrates the particle nature of light o There is a minimum frequency of light until electrical current occurs Amount of current was proportional with intensity of light shown on it o Classical theory said that E if ejected e- should increase with rise is light intensity, it was not observed o No e- observed until light of a minimum E was used o Light consists of particles called photons of discrete energy o Calculate E of 100 mol of photons of red light lambda = 700 nm nu = 4.29 x 10^14 sec^-1 Lambda = (6.626 x 10^-34 J(s)) (4.29 x 10^14 s^-1) = 2.85 x 10^-19 J per photon 2.85 x 10^- 6.022 x 10^23 19 J photons/mol = 171.6 kJ/mol Enough energy to break bonds Excited gases and atomic structure o Electricity off --> colorless o Electricity on --> excited electrons = color Atomic emission spectra and Niels Bohr o Bohr's greatest contribution was building a simple model of the atom Based off of an understanding the sharp emission spectra Line emission spectra and excited atoms o Excited atoms emit light of only certain wavelengths o Wavelength of emitted light depend on element Visible series in H atom spectrum are called Balmer series Rydberg equation o Balmer and rydberg worked on a math equation to calculated the wavelengths of all spectrial lines of H+ 1/lambda = (R_h)((1/n_1)^2 - (1/n_2)^2) R_h is constant = 1.096676 x 10^7 m^-1 N_1 and N_2 are positive integers, n_2 > n_1 Atomic spectra and Bohr o Early 20th century was that e- traveled about the nucleus in orbit Any orbit should be possible and so is any energy But changed particles moving in electric field should emit energy and orbit will eventually decay End result is destruction o Bohr: classical view is wrong Quantum or wave mechanics o E- can only exist in certain discrete locations (stationary states) o E- restricted to quantized energy states Fixed amount of E E_n = -R_h (h x c/n^2) = (-2.18 x 10^-18 J) (1/n^2) o E of state = -c/n^2 N = quantum number o Bohr showed that energy possessed by a single e- in one nth orbit or energy level of the H atom was given o R_h = ryberg's constant, h = planck's constant, c = speed of light o Only orbit where n = integral A are permitted o Radius allowed orbitals is proportional to n^2 o If e-'s are in quantized energy states, the delta E of states can have only certain values: explain sharpness of the line spectra o Calculate delta E = E final = E initial = -C [(1/n_f^2) - (1/n_i^2)] N=2 and to n=1 Delta E = -C [(1/1 ^2) - (1/2 ^2)] =-3/4 C EXOTHERMIC PROCESS Delta E= -3/4 C C= 2.18 x 10^-18 J --> E of emitted light -3/4(2.18 x 10^-18 J) -1.64 x 10^-18 J E = h x nu --> 1.64 x 10^-18 J = (6.626 x 10^-34 J(s)) nu Nu = 2.47 x 10^15 s^-1 Lambda = c/nu --> 1.12 x 10^-7 m x c = 121 nm o Bohr's theory was accomplished Noble prize 1922 Problems with theory Only successful for H Introduced quantum idea artifically Quantum/wave mechanics o L.De Broglie (1924) proposed that all moving objects have wave properties o For light: E = mc^2, E= h(nu) = hc/lambda Therefore, mc^2 = hc/lambda --> mc = h/lambda o More generally for particles with mass (m) moving at velocity (v) Mass x velocity = h/lambda Or lambda = h/mv o Wave particle duality: an e- has properties of both o E Schroedinger applied idea of e- behavior as a wave to the problem of e- in atoms --> develops wave equation o Solution gives in expression called wave function (Y) o Each describes an allowed energy state of e- Quantization into naturally Uncertainty principle o W Heisenberg: problem with defining nature of e- in atoms o Can't simultaneously define the position and momentum of e- o Define e-'s energy exactly but accept the limitation Wave Function (Y) o Each Y corresponds to orbital --> region of space within an e- is forced o Doesn't describe exact location --> proportional Quantum numbers and atomic orbitals o An allowed electron energy state (orbital) is defined by 3 quantum numbers o The principal quantum number (n) is a positive integer The value of n indicates the relative size of the orbital and therefore its relative distance from the nucleus o The angular momentum quantum number (l) is an integer from 0 to (n- 1) The value of l indicates the shape of the orbital o The magnetic quantum number (m_1) is an integer with values from -l to +l The value of m_1, indicates the spatial orientation of the orbital Allowed values of quantum numbers o N = the number of subshells in a shell ( l=0 to n-1) N=1 l=0 N=2 l= 0,1 N-3 l=0,1,2 o 2l+1 = the number of orbitals in a given subshell = the number of values of m_1 (m_1 = -l,..0,…+l) L=0, m_1=0 L=1, m_1= -1,0,+1 L=2, m_1= -2,-1,0,+1,+2 o N^2 = the total number of orbitals in a shell (all orbitals in all subshells) o Name, symbol (property) Allowed values Principal, n (size, energy) Positive integer (1,2,3…) Angular momentum, l 0 to n-1 (shape) Magnetic, m_1 -l…0…+l (orientation) Subshells = different atomic orbital types o Orbital names come from descriptions of line spectra: s= "sharp" p= "principal", d= "diffuse", f= "fundamental" Naming subshells (sublevels) o L = 0 is an s subshell o L = 1 is a p subshell o L = 2 is a d subshell o L = 3 is a f subshell o L = 4 is a g subshell Subshells = different atomic orbital types o Sublevel "name" = n value + letter designation 3s or 2p Shells and subshells o When n= 1, then l o M_l has a single value --> 1 orbital This subshell is labeled 1s o Every shell has 1 orbital labeled s, and it is a spherical in shape S orbitals o All s orbitals are spherical in shape P orbitals o When n=2 then l=0 and 1 o Therefore, in n=2 shell there are 2 types pf orbitals - 2 subshells o For l=0, m_l=0 This is a subshell o For l= 1, m_1 = -1, 0, +1 This is a p subshell with 3 orbitals o When l=1, there is a single planar node through the nucleus o The three orbitals lie 90 degrees apart in space D orbitals o When n=3, what are the values of l? L = 0, 1, 2 So there are 3 subshells in the shell o For l=0, m_l=0 S subshell with single orbital o For l=1, m_l=-1, 0, +1 P subshell with 3 orbitals o For l=2, m_l= -1, -1, 0 ,1, 2 D subshell with 5 orbitals o S orbitals have mo planar node (l=0) and so are spherical o P orbitals have l=1, and have 1 planar node Dumbbell shaped o This mean d orbitals (with l =2) have 2 planar nodes F orbitals o When n=4, l=0, 1, 2, 3 so there are 4 subshells in the shell o For l=0, m_l=0 S subshell with single orbital o L=1, m_l= -1, 0, 1 P subshell with 3 orbitals o L=2, m_l= -2, -1, 0, 1, 2 D subshell with 5 orbitals o L=3 m_l= -3, -2, -1, 0, 1, 2, 3 F subshell with 7 orbitals o The F_xyz orbital, one of seven f orbitals
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