CHEMICAL BOND & SPECTROSCOPY I CHM6470

CHEMICAL BOND & SPECTROSCOPY I CHM6470 Prof. Valeria D. Kleiman Office 311A CLB Tel: 392-4656 e-mail: kleiman@chem.ufl.edu CLASS WEBSITE www.chem.ufl.edu/~kleiman/6470 Meeting time and place MWF 10:40-11:30 am CLB 313 "Elements of Quantum Mechanics" by Mike Fayer. Oxford University Press ISBN 0 19 514195 4

Grading • homework (about 10-12) (35%) • 2 progress tests (30%) • term paper (15%) Due November 22nd • biographical paper (5%) Due October 17th • class participation (15%)

QM Description of the behavior of particles @ the atomic scale Absolute vs Relative size CM: Size is relative  There is always a measurement which produces a disturbance small enough not to change the object QM: Size is absolute  There is a limit to the disturbance used for a measurement. At some point, the object is so small that we cannot measure it without disturbing it!

Experiment with bullets 1 2 Detector moves in x direction Bullets do not break  detector sees always WHOLE bullets. If gun’s firing rate is slower, we detect less WHOLE bullets, but never ½ bullet  Bullets arrive in identical “lumps” Measure the # bullets arriving at x, by unit time  P(x)

Bullets If slit 1 is closed and 2 is open What is the probability that a bullet which passes through the holes 2 will arrive at xn? P2 The max of P2 is aligned with slit 2 1 2 P2

Bullets If slit 2 is closed and 1 is open What is the probability that a bullet which passes through the holes 2 will arrive at xn? P1 The max of P1 is aligned with slit 1 P1 1 2

Bullets P12= P1+P2 1 2 If slit 1 and 2 are open What is the probability that a bullet which passes through either hole 2 will arrive at xn? P12 The max of P12 is aligned in the center P12= P1+P2

Experiment H2O waves Detector measures the height of the wave when it arrives at xn  Intensity = h2 = rate at which energy reaches the detector Intensity can vary CONTINUOUSLY  No “lumps” 1 2

Waves If slit 1 is closed and 2 is open What is the intensity measured at xn? I2 = |h2| 1 2 I2

Waves If slit 2 is closed and 1 is open What is the intensity measured at xn? I1 = |h1| 1 I1 2

Waves xa, in phase Individual peaks add I12  xb out of phase Individual peaks cancel each other I12  I12 I1+I2 If slit 2 and 1 are open What is the intensity measured at xn? 1 2

Waves Interference 1 2

Experiment with electrons 1 2 Source: electron gun, tungsten wire heated by current, wall at – voltage Detector: geiger or e- multiplier connected to a speaker It clicks every time an e- reaches the detector, making a sound

Electrons 1 2 Clicks are not uniformly distributed  “average rate” At different positions, we hear a different rate, but the volume (size) of each click is always the same T  the rate is , but volume is = (same size) T  the rate is , but volume is = (same size) If there are 2 detectors, you never hear 2 clicks at the same time  e- behaves as “lumps” WHOLE e- arrives at the detector

Electrons If slit 2 is open and 1 is closed What is the probability that an e- which passes through hole 2 will arrive at xn? P2 1 2 P2

Electrons If slit 2 is closed and 1 is open What is the probability that an e- which passes through hole 1 will arrive at xn? P1 P1 1 2

Electrons 1 2 INTERFERENCE PATTERN! If both slits are open…

How do we explain the interference? • Possibility 1 • e- do not go through slit 1 or slit 2, but they “split” between the 2 slits • NOT TRUE, e- always arrive in “lumps” (one click, same volume) • Possibility 2 • Closing one slit increases the P of e- going through the other slit • NOT TRUE, at x=0, P1< ½ P12  When we closed 2, P1 did not increased If we recall the math associated with waves, we say that Pe-1= |f1|2Pe-2= |f2|2and Pe-12= |f1+ f2|2 • e-arrive in “lumps” like particles probability of arrival has interference  like waves

Watching electrons We watch the e- by adding a strong light source after they go through the slit Scattered light (flash) above x=0  Slit 1 Scattered light (flash) below x=0  Slit 2 1 2 One click  one flash and One flash one click e- go EITHER through 1 or 2

Watching electrons P1’ P2’ We count : number of e- that went through Slit 1  P1’ (same as P1, when slit 2 is closed) number of e- that went through Slit 2  P2’ (same as P1, when slit 1 is closed) 1 2 When we are “watching”, e- come through just as expected! P12= P1 +P2

Watching electrons P12 P1 +P2 Turn of the light and when we are “ not watching 1 2 light e- interaction changes the motion of the e-

Watching electrons One flash one click but sometimes One click  NO flash light behaves in “lumps” Since watching the e- changes their motion, we try to look with a dim dim dim light source, so the interaction will not disturb the e- motion 1 2 If brightness  , the number of flashes goes  , but if there is a flash, it is always the same

Watching electrons We count : number of e- that went through Slit 1  P1” (same as P1, when slit 2 is closed) number of e- that went through Slit 2  P2” (same as P1, when slit 1 is closed) P1” 1 2 P2”

Watching electrons We count : number of e- that did not give a flash  P”12  INTERFERENCE! 1 2

Watching electrons We can try keeping the brightness constant, changing only the l (longer l smaller momentum  less disturbance? 1 2

Watching electrons We can try keeping the brightness constant, changing only the l (longer l smaller momentum  less disturbance? 1 2 For l ~ xslit 1-xslit 2 the flash becomes LARGE and FUZZY We cannot say whether the flash came from above or below x=0 For l < xslit 1-xslit 2  NO INTERFERENCE For l > xslit 1-xslit 2  INTERFERENCE

Absolute size It is IMPOSSIBLE to design an apparatus to determine through which slit the e- goes THAT WILL NOT at the same time DISTURB the e- enough to DESTROY the INTERFERENCE pattern QM: Size is absolute  There is a limit to the disturbance used for a measurement. At some point, the object is so small that we cannot measure it without disturbing it! If we look, we can say that the e- goes either through 1 or 2 If we don’t look, we may not say that it goes through 1 or 2

Summary • Probability of an event is given by |f|2 where f is a complex number (probability amplitude) • When an experiment can occur in alternative ways  INTERFERENCE f =f1+ f2 P = |f1 + f2|2 • If we determine WHICH pathway was taken  INTERFERENCE IS LOST

Back to bullets 1 2 The associated l is so small, that the interference pattern is smoothed out. The resolution in P12 is not goof enough to see the peaks and valleys Why the bullets did not give interference pattern?

Wave/particles What is the relation between those wave/particle properties? Each particle has an associated l. DeBroglie, (1924) proposed that particles with rest mass have • bullet (0.2 gr 500m/s) ~ 6.626x10-33m To obtain an interference pattern, we would need slits separated by 10-33m h defines the granular composition of our universe

State of a system transmission || No transmission  a • State: a description of a system with as many conditions as theoretically possible without contradictions I transmitted = I || = Io I transmitted = I  = 0 I transmitted = Io cos2a

Light as particles how much P|| or P is contained in Pa If we can measure 1 photon at the time: Input photon is polarized ||  light is transmitted, and output is || Input photon is polarized  light is NOT transmitted Input photon is polarized with angle a???? Observation: Sometimes the WHOLE photon is transmitted, and it is //polarized Sometimes nothing is transmitted Question: Is the photon jumping between polarizations? Answer: Superposition of states Any polarization Pa can be expressed as a superposition of 2 perpendicular states

Projection When photons are observed, they are “forced”to be in either || or  polarization If we look, we can say that the photon is either|| or  If we don’t look, we may not say that it is || or  Each individual observation will be either || or , but after many observations, cos2a of those measurement will be || a is a state of polarization, which can also be described as sum of 2 other states (|| and )

CHEMICAL BOND & SPECTROSCOPY I CHM6470