GENERAL CHEMISTRY 1140

QUANTIZATION OF ELECTRONS

BOHR ATOM

 

1873 - MAXWELL - LIGHT IS AN ELECTROMAGNETIC WAVE

1900 - PLANCK - LIGHT IS QUANTIZED
RADIATION FROM HOT BODIES

1905 - EINSTEIN - LIGHT IS A PARTICLE (PHOTON)
PHOTOELECTRIC EFFECT

1885 - BALMER - ATOMIC SPECTRUM OF HYDROGEN
BEING A MATHEMATICIAN, LOOKED FOR AN EQUATION
 

THE NUMBERS: n1 = 1, 2, 3, etc.; n2 = 2, 3, 4, 5, ETC., HAD NO PHYSICAL MEANING
    THEY JUST WORKED.
    PLUG TWO WHOLE NUMBERS IN AND YOU GET THE FREQUENCY OF AN OBSERVED WAVELENGTH!!.
    WE NOW CALL THESE NUMBERS "QUANTUM NUMBERS".

BOHR'S PLANETARY MODEL OF THE ATOM (1913)

ELECTRONS ORBIT THE NUCLEUS
    LIKE PLANETS ORBIT THE SUN

ONLY CERTAIN ORBITS ARE ALLOWED (QUANTIZED!)

BASED ON NEWTON'S LAWS OF MOTION AND ELECTROSTATICS

UPON HEATING, ELECTRON GOES TO A HIGHER ENERGY ORBIT

ELECTRON FALLS BACK TO LOWER ENERGY ORBIT AND EMITS ENERGY AS A PHOTON

 

 

EXCITATION-EMISSION SIMULATION

 

 

IF YOU SOLVE BOHR'S EQUATION FOR THE FREQUENCY, YOU GET BALMER'S EQUATION!

BOHR'S ORBIT THEORY ALLOWED ONE TO PREDICT HYDROGEN SPECTRA QUITE WELL. BUT WHY WERE ONLY CERTAIN ORBITS ALLOWED?

DE BROGLIE (1924) SAID ELECTRONS BEHAVE AS STANDING WAVES

THE WAVELENGTH IS RELATED TO QUANTUM NUMBER n AND THE RADIUS r

AND FURTHER PROPOSED WAVELENGTH RELATED TO MASS, VELOCITY, AND PLANCK'S CONSTANT

A FEW YEARS LATER IT WAS DEMONSTRATED THAT ELECTRONS ARE DIFFRACTED BY METAL FOILS MUCH LIKE X-RAYS.

LIGHT IS FOUND TO HAVE WAVE AND MATTER (PHOTON) PROPERTIES

ELECTRONS ARE FOUND TO HAVE MATTER AND WAVE PROPERITES

NEW PHYSICS!!

NOTE: MANY OF THE NEW IDEAS CAME ON THE HEELS OF OTHER NEW IDEAS
 

 

A GREAT MODEL WITH A FEW PROBLEMS

IT WORKS FOR H, He1+, Li2+, BUT VERY FEW OTHER SPECIES!

    IT APPEARS TO ONLY DESCRIBE THE INTERACTION BETWEEN ONE ELECTRON AND A POSITIVE NUCLEUS

    IT DOES NOT WORK FOR TWO OR MORE ELECTRONS!

IT IMPLIES THAT WE KNOW THE "POSITION" OF A WAVE

IT VIOLATES HEISENBERG'S UNCERTAINTY PRINCIPLE

    HEISENBERG - IT IS IMPOSSIBLE TO KNOW SIMULTANEOUSLY BOTH THE MOMENTUM (p = m v) AND THE POSITION OF A PARTICLE WITH CERTAINTY.

HEISENBERG'S UNCERTAINTY PRINCIPLE (PARAPHRASED)

    IF WE KNOW WHERE IT'S AT, WE DON'T KNOW WHERE IT IS GOING.

    IF WE KNOW WHERE IT'S GOING, WE DON'T KNOW WHERE IT'S AT.

BOHR'S MODEL SAYS WE KNOW BOTH - A VIOLATION

 

SCHRODINGER'S MODEL OF THE ATOM (1926)

FORMULATED AN EQUATION WHICH DESCRIBES THE PARTICLE AND WAVE PROPERTIES OF AN ELECTRON

    WAVE FUNCTION Y HAS NO PHYSICAL MEANING

    BUT Y2 GIVES THE PROBABILITY OF FINDING AN ELECTRON IN THE SPACE DEFINED

    SOLVE Y2 FOR WHOLE UNIVERSE AND THE PROBABILITY OF FINDING THE ELECTRON IS 1 (USELESS CALCULATION)

    SOLVE Y2 SO THAT THE PROBABILITY OF FINDING THE ELECTRON IS 0.9 (90%) AND CALL THIS VOLUME AN "ORBITAL".

    TWO DEFINITIONS

      AN ORBITAL IS A REGION IN SPACE WHERE THE PROBABILITY OF FINDING THE ELECTRON IN QUESTION IS HIGH (90%)

      AN ORBITAL IS A REGION IN SPACE WHERE THE ELECTRON WAVE DENSITY IS HIGH (90%)

CAN BE SOLVED FOR THE H ATOM AND OTHER ONE ELECTRON IONS

CAN'T BE SOLVED EXACTLY FOR 2+ ELECTRON SYSTEMS

CAN BE SOLVED APPROXIMATELY FOR 2+ ELECTRON SYSTEMS

    GIVES RESULTS CONSISTANT WITH OBSERVATIONS SO WE WILL USE IT!

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