Copyright Sautter 2003

ATOMIC STRUCTURE

QUANTUM THEORY

&

ELECTRONIC CONFIGURATION

OF ATOMS

SUBATOMIC STRUCTURE

• ALL ATOMS CONSIST OF PROTONS, NEUTRONS AND ELECTRONS

• PROTONS ARE POSITIVELY CHARGED PARTICLES THAT RESIDE IN THE NUCLEUS AT THE CENTER OF THE ATOM

• NEUTRONS ARE PARTICLES WITH NO CHARGE THAT ALSO ARE CONTAINED IN THE NUCLEUS.

• ELECTRONS ARE NEGATIVELY CHARGED PARTICLES THAT ARE EXTERNAL TO THE NUCLEUS.

SUBATOMIC STRUCTURE

• The experiments of Ernest Rutherford in the early 1900s, showed that matter consisted of small, highly concentrated, points of matter (the nucleus) surrounded by vast areas of empty space (the areas where electrons exist).

• This is called the “Empty Space Model” of the atom. • Rutherford shot high energy alpha particles at a gold

foil. The alpha particles acted as “bullets”. Most all the alpha particles went straight through. A few were deflected.

• From this experiment, Rutherford concluded that tiny points of concentrated mass, distributed in mostly empty space, was the fundamental structure of matter.

RUTHERFORD’S EXPERIMENT(A CLOSE UP)

A FEWALPHA

PARTICLESARE DEFLECTED

GOLD FOIL

PARTICLES

MOST TRAVELSTRAIGHT

THROUGH THEMETAL

= NUCLEUS

MOST OF THE ATOM IS EMPTY SPACE

WHAT MAKES ONE ATOM DIFFERENT FROM ANOTHER ?

• EACH ELEMENT HAS DIFFERING NUMBERS OF PROTONS. THIS IS WHAT MAKES ELEMENTS DIFFERENT, THE NUMBER OF PROTONS IT CONTAINS.

• THE ATOMIC NUMBER OF AN ELEMENT TELLS US THE NUMBER OF PROTONS IT CONTAINS. ELEMENTS ON THE PERIODIC TABLE ARE ARRANGED IN ROWS, LEFT TO RIGHT IN ORDER OF INCREASING ATOMIC NUMBER. THEY START WITH HYDROGEN, ATOMIC NUMBER 1, FOLLOWED BY HELIUM, ATOMIC NUMBER 2, LITHIUM ATOMIC NUMBER 3, ETC.

WHAT ABOUT THE NUMBER OF NEUTRONS IN AN ATOM ?

• THE NUMBER OF NEUTRONS VARY FROM ELEMENT TO ELEMENT. SOME ATOMS OF THE SAME ELEMENT MAY HAVE DIFFERENT NUMBERS OF NEUTRONS. ATOMS OF THE SAME ELEMENT WITH DIFFERENT NEUTRON NUMBERS ARE CALLED ISOTOPES.

• THE ATOMIC MASS TELLS US THE COMBINED NUMBER OF PROTONS AND NEUTRONS IN THE AVERAGE ATOM (ISOTOPE) OF THAT ELEMENT.

CALCULATING THE NUMBER OF NEUTRONS IN AN ATOM

• THE ATOMIC NUMBER OF THE ELEMENT SODIUM (Na) IS 11 AND ITS ATOMIC MASS IS 22.99. WE’LL ROUND THIS NUMBER TO 23. SINCE THE ATOMIC NUMBER TELLS THE NUMBER OF PROTONS, SODIUM MUST HAVE 11 PROTONS. THE PROTONS AND NEUTRONS TOGETHER EQUAL 23. BY SUBTRACTION, SODIUM MUST HAVE 12 NEUTRONS IN AN AVERAGE ATOM OF SODIUM.

• WHAT ABOUT AN ATOM LIKE CHLORINE? ITS ATOMIC MASS IS 35.45. ITS ATOMIC NUMBER IS 17. IT THEREFORE HAS 17 PROTONS, BUT SUBTRACTING 17 FROM 35.45 GIVES 18.45. HOW COULD AN ATOM HAVE .45 NEUTRONS??

HAVE YOU FIGURED OUT THE ANSWER ??

• REMEMBER, THE ATOMIC MASS IS THE AVERAGE OF THE DIFFERENT ISOTOPES OF THAT ELEMENT. NO ONE ATOM HAS A MASS OF 35.45. INSTEAD, SOME CHLORINE ATOMS HAVE MASSES OF 35, SOME 36, SOME 37.

• SO CHLORINE ATOMS OF MASS 35 HAVE 18 NEUTRONS, THOSE OF MASS 36 HAVE 19 NEUTRONS AND THE MASS 37 ATOMS HAVE 20 NEUTRONS.

• THERE IS STILL A QUESTION HOWEVER. THE AVERAGE OF 35, 36 AND 37 IS NOT 35.45, IT IS 36. WHY ISN’T 36 LISTED AS THE ATOMIC MASS NUMBER FOR CHLORINE ?

WHY NOT A MASS NUMBER OF 36 THEN ?

• IN ORDER TO GET 36 AS AN AVERAGE THERE MUST BE EQUAL NUMBERS OF ATOMS OF ALL THREE ISOTOPES OF CHLORINE PRESENT. THIS EQUAL DISTRIBUTION IS RARELY TRUE FOR ANY ELEMENT IN NATURE.

• HERE IS ANOTHER EXAMPLE. HYDROGEN ATOMS OCCUR AS THREE DIFFERENT ISOTOPES, HYDROGEN WITH AN ATOMIC MASS OF 1, DEUTERIUM, THAT IS HYDROGEN WITH A MASS OF 2 AND FINALLY TRITIUM, HYDROGEN WITH A MASS NUMBER OF 3. ON THE PERIODIC TABLE THE ATOMIC MASS OF HYDROGEN IS LISTED AS 1.0079, ALMOST 1. CAN YOU EXPLAIN WHY THE LISTED MASS NUMBER IS SO CLOSE TO ONE INSTEAD OF THE ARITHEMATIC AVERAGE OF TWO?

ARITHEMATIC AVERAGES AND WEIGHTED AVERAGES ARE DIFFERENT. THE ATOMIC MASS IS A WEIGHTED AVERAGE OF THE

ISOTOPES FOR THAT ELEMENT !

• HYDROGEN 1 (IT HAS 1 PROTON AND NO NEUTRONS) REPRESENTS 99.985 % OF ALL HYDROGEN ATOMS

• HYDROGEN 2 (IT HAS 1 PROTON AND 1 NEUTRON) REPRESENTS ONLY 0.015 % OF ALL HYDROGEN ATOMS.

• HYDROGEN 3 (IT HAS 1 PROTON AND 2 NEUTRONS) REPRESENTS 0.0001 % , ALMOST NO HYDROGEN ATOMS.

• THE WEIGHTED AVERAGE CONSIDERS THAT MOST ALL HYDROGEN ATOM HAVE A MASS OF 1 AND THEREFORE THE NUMBER APPEARING ON THE PERIODIC TABLE IS VERY, VERY CLOSE TO 1.00

THE ATOMIC MASS NUMBERS ON THE PERIODIC TABLE THEN ARE WEIGHTED AVERAGES WHICH

ACCOUNT NOT ONLY FOR THE MASSES OF DIFFERENT ISOTOPES, BUT ALSO ACCOUNTS FOR

ABUNDANCE (PERCENT) AT WHICH THEY OCCUR IN NATURE !!

THE AVERAGES WHICH YOU ARE USED TO WORKING WITH IN MATH CLASS ARE ARITHEMATIC

AVERAGES WHICH DO NOT ACCOUNT FOR ABUNDANCES.

SO FAR THEN, THE NUMBER OF PROTONS IN THE NUCLEUS OF AN ATOM EQUALS THE ATOMIC

NUMBER AND THE NUMBER OF NEUTRONS EQUAL THE ATOMIC MASS MINUS THE ATOMIC NUMBER

• WHAT ABOUT THE NUMBER OF ELECTRONS ??

• WELL, THIS DEPENDS ON WHETHER WE ARE TALKING ABOUT A NEUTRAL ATOM OR AN ION !

• IN A NEUTRAL ATOM THE NUMBER OF ELECTRONS AND PROTONS ARE EQUAL, SO THE NUMBER OF ELECTRONS EQUALS THE ATOMIC NUMBER OF THAT ATOM.

• IN THE CASE OF IONS THE NUMBER OF ELECTRONS IS DIFFERENT THAN THE ATOMIC NUMBER.

WHAT IS AN ION ?WHAT ARE THE TWO KINDS OF IONS ?

• IONS ARE ATOMS OR GROUPS OF ATOMS WITH EXTRA OR MISSING ELECTRONS.

• ATOMS WITH EXTRA ELECTRONS ARE IONS WITH A NEGATIVE CHARGE AND ARE CALLED ANIONS.

• ATOMS WITH MISSING ELECTRONS ARE IONS WITH A POSITIVE CHARGE AND ARE CALLED CATIONS. IT IS IMPORTANT TO UNDERSTAND HERE THAT CATIONS DO NOT HAVE EXTRA PROTONS, THAT IS THEY DO NOT AND CAN NOT GAIN PROTONS. IF THEY COULD THEY WOULD BE COME A DIFFERENT ELEMENT. THE NUMBER OF PROTONS AN ATOM CONTAINS MAKES THE ATOM WHAT IS IT !!

LET’S DETERMINE THE ATOMIC STRUCTURE FOR OXYGEN

• OXYGEN IS ELEMENT WITH AN ATOMIC NUMBER OF 8 AND AN ATOMIC MASS NUMBER OF 16 (OXYGEN OCCURS AS THREE DIFFERENT ISOTOPES 16, 17 AND 18. SINCE THE MASS NUMBER IS SO CLOSE TO 16, MOST ALL OXYGEN ATOMS (99.8 %) ARE ISOTOPE 16).

• THE MOST COMMON ATOM OF OXYGEN THEN CONSISTS OF 8 PROTONS AND (16 – 8) OR 8 NEUTRONS IN THE NUCLEUS. IF THE ATOM IS NEUTRAL IT THEN ALSO CONTAINS 8 ELECTRONS EXTERNAL TO THE NUCLEUS.

WHEN ATOMS COMBINE TO FORM MOLECULES THE ELECTRONS OF EACH

ATOM MUST FIRST INTERACT.

• HOW ARE THE ELECTRONS ARRANGED IN THE ATOM ? UNDERSTANDING THIS HELPS US TO DISCOVER HOW AND WHY ATOMS COMBINE!

• ELECTRON ARRANGEMENTS WITHIN ATOMS ARE REFERRED TO AS ELECTRON CONFIGURATIONS.

• BEFORE WE CAN UNDERSTAND ELECTRON CONFIGURATIONS, WE MUST FIRST UNDERSTAND HOW THEY WERE DISCOVERED IN THE FIRST PLACE. THIS REQUIRES THE USE OF A SCIENCE CALLED QUANTUM MECHANICS.

BASIC CONCEPTS OF QUANTUM MECHANICS

• ELECTRONS EXIST IN AREAS OUTSIDE THE NUCLEUS. THESE AREAS ARE CALLED ENERGY LEVELS. YOU MIGHT HAVE HEARD OF THEM BEFORE AS “SHELLS”. THERE ARE NUMEROUS ENERGY LEVELS AT WHICH THE ELECTRON CAN BE FOUND, EACH AT A PROGRESSIVE HIGHER ENERGY.

• THESE LEVELS ARE ASSIGNED NUMBERS 1,2,3, ETC. AS THE NUMBER INCREASES, THE ENERGY STATE OF THE ELECTRON BECOMES HIGHER.

BASIC CONCEPTS OF QUANTUM MECHANICS (CONT’D)

• AN ORIGINAL ATOMIC THEORY PROPOSED BY NEILS BOHR IN THE EARLY 20TH CENTURY SUGGESTED THAT ELECTRONS CIRCLE THE NUCLEUS OF ATOMS IN ORBITS SIMILAR TO THE PATHS OF THE PLANETS AROUND THE SUN.

• A MOST IMPORTANT CONCEPT OF MODERN QUANTUM

THEORY IS HOWEVER, THAT ELECTRONS DO NOT MOVE IN ORBITS ABOUT THE NUCLEUS OF THE ATOM !!

THE ENERGY LEVELS OF ATOMS ARE NOT ORBITS FOR

ELECTRONS. THEY ARE AREAS OF HIGH PROBABILITY OF FINDING ELECTRONS.

ELECTRON

ORBITS !!NEILS BOHR

BASIC CONCEPTS OF QUANTUM MECHANICS (CONT’D)

• WHEN ENERGY (HEAT, ELECTRICITY, ETC.) IS ADDED TO AN ATOM, THE ELECTRONS WITHIN THE ATOM JUMP TO HIGHER ENERGY LEVELS.

• WHEN THE ELECTRONS FALL BACK TO THEIR ORIGINAL ENERGY LEVEL, THEY RELEASE THE ENERGY THAT THEY ABSORBED IN THE FORM OF LIGHT.

• THEREFORE, IN ORDER TO UNDERSTAND THE ELECTRONIC STRUCTURE OF THE ATOM WE MUST FIRST UNDERSTAND THE NATURE OF LIGHT ITSELF! WAVES &

ORBITALSIRWIN SCHROEDINGER

QUANTUM MECHANICS GENIUS

LIGHT – A WAVE AND A PARTICLE

• LIGHT MAY THOUGHT OF AS A WAVE IN SOME CASES AND AS A PARTICLE IN OTHERS. WHICH ONE IS IT REALLY? BOTH !!

• LET’S TALK ABOUT WAVES FIRST. IMAGINE A WATER WAVE TO START. ALL WAVES HAVE THREE BASIC PROPERTIES. CAN YOU NAME ONE?

• (1) WAVELENGTH

• (2) FREQUENCY

• (3) SPEED OR VELOCITY

MORE ABOUT WAVES• WHAT IS WAVELENGTH ?• THE DISTANCE REQUIRED FOR ONE COMPLETE WAVE TO

OCCUR. ITS SYMBOL IS THE GREEK LETTER , , “LAMBDA” AND IT IS MEASURED IN METER PER WAVE. IT COULD BE MEASURED FROM THE CREST OF ONE WAVE TO THE CREST OF THE NEXT, OR THE TROUGH OF ONE TO THE NEXT, AS LONG AS THE LENGTH OF ONE COMPLETE WAVE IS MEASURED.

• WHAT IS FREQUENCY ?• IT IS EXACTLY WHAT IS SAYS, HOW FREQUENTLY DO

WAVE COME BY. FOR EXAMPLE, HOW MANY WAVES HIT THE SHORE IN A SECOND! THAT IS THE WAVE’S FREQUENCY. WE USE THE GREEK LETTER, , “NU” AS THE SYMBOL FOR FREQUENCY AND IT IS MEASURED IN WAVES PER SECOND. ( A WAVE PER SECOND IS CALLED A HERTZ)

MORE ABOUT WAVES (CONT’D)• SPEED OR VELOCITY AS YOU PROBABLY KNOW, TELLS US

HOW FAR THE WAVE GOES IN A SECOND. THE WAVES THAT WE WILL BE TALKING ABOUT, AS SAID BEFORE, ARE LIGHT WAVES. THE SPEED OF LIGHT WAVES IS VERY, VERY FAST, ABOUT 186,000 MILES PER SECOND !

• THAT IS 3.0 x 108 METER PER SECOND.

• “C” IS THE SYMBOL USED FOR THE SPEED OF LIGHT

(C = 3.0 x 108 METERS / SECOND)

MORE ABOUT WAVES (CONT’D)

• HOW ARE WAVELENGTH, FREQUENCY AND THE SPEED OF A WAVE RELATED ?

• THE UNITS FOR WAVELENGTH ARE METERS / WAVE

• THE UNITS FOR FREQUENCY ARE WAVES / SECOND

• THE UNITS FOR SPEED ARE METERS / SECOND

• (METERS / WAVE) x (WAVES / SEC) = METERS / SEC

• WAVELENGTH x FREQUENCY = SPEED

• x = C• REMEMBER C IS THE SPEED OF LIGHT• 3.0 x 108 METERS / SECOND

VISIBLE AND INVISIBLE LIGHT• MOST “LIGHT” IS NOT VISIBLE TO THE HUMAN EYE !

• ONLY ABOUT 7 % OF THE KNOWN KINDS OF LIGHT CAN BE SEEN WITHOUT SPECIAL INSTRUMENTATION.

VISIBLE AND INVISIBLE LIGHT

• THE VISIBLE SPECTRUM INCLUDES ALL THE COLORS OF THE RAINBOW, ROYGBIV, RED, ORANGE, YELLOW, GREEN, BLUE, INDIGO AND VIOLET !

• EACH COLOR AND EACH KIND OF LIGHT CAN BE INDENTIFIED BY ITS WAVELENGTH AND / OR FREQUENCY.

• THE RED END OF THE SPECTRUM HAS THE LONGEST WAVELENGTH AND LOWEST FREQUENCY IN THE VISIBLE RANGE.

• THE VIOLET END HAS THE SHORTEST WAVELENGTH AND HIGHEST FREQUENCY.

• AS WAVELENGTH INCREASES, FREQUENCY DECREASES, THEY ARE INVERSE TO EACHOTHER

•

VISIBLE AND INVISIBLE LIGHT (CONT’D)

• THE WAVELENGTH OF RED LIGHT IS APPROXIMATELY 7.20 x 10-7 METERS OR 720 NANOMETERS

• THE WAVELENGTH OF VIOLET LIGHT IS APPROXIMATELY 3.80 x 10-7 METERS OR 380 NANOMETERS

• INFRARED (BELOW RED) OR IR CONSISTS FREQUENCIES LOWER THAN RED (AND > 720 NM) AND ULTRAVIOLET (ABOVE VIOLET) OR UV CONSISTS OF FREQUENCIES HIGHER THAN VIOLET (AND < 320 NM).

• ALTHOUGH BOTH INVISIBLE, INFRARED CAN BE FELT AS HEAT AND ULTRAVIOLET FROM THE SUN CAUSES SUNBURN.

• IN ORDER TO BE MEASURED, IR AND UV REQUIRE DETECTORS TO BE USED

CALCULATIONS INVOLVING LIGHT WAVES

• THE WAVELENGTH OF GREEN LIGHT IS APPROXIMATELY 5.5 x 10-7 METERS. WHAT IS ITS FREQUENCY ?

• SOLUTION: WE KNOW AND ARE INVERSELY PROPORTIONAL BY THE EQUATION

x = C AND C = 3.0 x 108 M / SEC

(5.5 x 10-7 M / WAVE) = 3.0 x 108 M /SEC

= 5.45 x 1014 WAVES / SEC OR HERTZ

CALCULATIONS INVOLVING LIGHT WAVES (CONT’D)

• WHAT COLOR IS LIGHT OF A FREQUENCY 3.75 x 1014 HZ ?

• SOLUTION: WE KNOW THE RANGE OF VISIBLE LIGHT IS BETWEEN RED ( = 7.2 x 10-7 METERS) AND VIOLET ( = 3.8 x 10-7 METERS). LET’S FIRST FIND THE OF FREQUENCY 3.75 x 1014 HZ !

• x = C

(3.75 x 1014 HZ) = 3.0 x 108 METER /SEC

= 8 x 10-7 METERS

THIS IS LONGER THAN RED THEREFORE THE LIGHT IS INFRARED AND INVISIBLE. IT HAS NO “COLOR”!

USING OUR KNOWLEDGE OF LIGHT TO UNDERSTAND ELECTRONIC STRUCTURE IN ATOMS

• RECALL FROM OUR PREVIOUS INFORMATION:

WHEN ATOMS ABSORB ENERGY, ELECTRONS JUMP TO HIGHER ENERGY LEVELS. WHEN THEY FALL BACK TO THEIR ORIGINAL ENERGY LEVELS, THAT ABSORBED ENERGY IS RELEASED AS LIGHT.

ANALYZING THIS EMITTED LIGHT ALLOWS US TO DISCOVER THE ELECTRONIC STRUCTURE OF THE ATOM!

BEFORE WE CAN DO THIS HOWEVER WE MUST FIRST INVESTIGATE THE SECOND NATURE OF LIGHT, THAT IS ITS PARTICLE NATURE !!

LIGHT PARTICLES, PLANCK AND PHOTONS

• PARTICLES OF LIGHT ARE CALLED “PHOTONS”. THESE ARE “PACKAGES” OF LIGHT ENERGY.

• MAX PLANCK WAS FIRST TO DISCOVER THE RELATIONSHIP BETWEEN THE WAVE NATURE OF LIGHT AND ITS PARTICLE NATURE.

• HE FOUND THAT THE ENERGY CONTENT OF LIGHT WAS DIRECTLY RELATED TO THE FREQUENCY OF THE LIGHT WAVE.

• THE EQUATION THAT MEASURES ENERGY AS A FUNCTION OF FREQUENCY IS:

ENERGY = A CONSTANT x FREQUENCY

E = h x

WERE h IS A CONSTANT CALLED

PLANCK’S CONSTANT (6.63 x 10-34 JOULES SEC / PHOTON)

PHOTONS

MR. PLANCK

EXPERIMENTAL PROOF OF THE PARTICLE NATURE

OF LIGHT IS FOUND IN THE PHOTOELECTRIC EFFECT.

WHEN LIGHT IS SHONE ON AN ACTIVE METAL SUCH

AS POTASSIUM ONLY LIGHT OF A CERTAIN MINIMUM

FREQUENCY WILL CAUSE ELECTRONS TO LEAVE THE

METAL SURFACE NO MATTER WHAT THE INTENSITY

OF THE LIGHT SOURCE. BASED ON THIS EXPERIMENT

THE ENERGY OF LIGHT IS FOUND TO BE CONTAINED

IN PACKAGES CALLED PHOTONS. THE ENERGY OF

THE PHOTONS OF A SPECIFIC KIND OF LIGHT IS

DIRECTLY RELATED TO ITS FREQUENCY.

THE PHOTOELECTRIC EFFECT AND PHOTONS

POTASSIUM METALBATTERY

VOLTMETERPHOTONS

PICKUP

WIREELECTRONS

ONLY CERTAIN MINIMUM FREQUENCIES OF LIGHT

FREE THE ELECTRONS FROM THE METAL

(ONLY PHOTONS WITH ENOUGH ENERGY)

THE PHOTOELECTRIC EFFECT EXPERIMENT

LIGHT PARTICLES, PLANCK AND PHOTONS

• RECALL THAT RED LIGHT HAS A WAVELENGTH OF 7.2 x 10-7 METERS AND A CORRESPONDING FREQUENCY OF 4.2 x 1014 HZ.

• VIOLET LIGHT HAS A WAVELENGTH OF 3.8 x 10-7 METERS AND A CORRESPONDING FREQUENCY OF 7.9 x 1014 HZ.

• E = h x

• USING PLANCK’S EQUATION, WE SEE THAT VIOLET CONSISTS OF HIGHER ENERGY PHOTONS BECAUSE OF ITS HIGHER FREQUENCY THAN DOES RED LIGHT WHICH IS OF A LOWER FREQUENCY.

LIGHT PARTICLES, PLANCK AND PHOTONS (CONT’D)

• SAMPLE PROBLEM:• WHAT IS THE ENERGY OF A PHOTON OF UV LIGHT WITH

WAVELENGTH, = 3.0 x 10-7 METERS ? • SOLUTION:

• REMEMBER: E = h x AND x = c• FIRST x = c, (3.0 x10-7) = 3.0 x 108

• = 1.0 x 10 15 HZ

• E = h x • E = (6.63 x 10-34 JOULES SEC / PHOTON) x 1.0 X 1015 HZ

E = 6.63 x 10-19 JOULES / PHOTON OF UV LIGHT

LIGHT PARTICLES, PLANCK AND PHOTONS (CONT’D)

• IN ADDITION TO LIGHT VERY HIGH VELOCITY SUBATOMIC PARTICLES (SUCH AS ELECTRONS) ALSO HAVE OBSERVEABLE WAVE PROPERTIES. THE WAVELENGTH OF THESE PARTICLE CAN BE CALCULATED USING THE DEBROGLIE EQUATION:

• = h / m x v WHERE h = PLANCK’S CONSTANT

(6.63 x 10-34 JOULE SEC/ PHOTON)

m = MASS IN KILOGRAMS

v = VELOCITY IN METERS / SEC

iiIF YOU’RE

MOVIN’

YOU’RE WAVEN’

DUDE!De Broglie

LIGHT PARTICLES, PLANCK AND PHOTONS (CONT’D)

• SAMPLE PROBLEM: ALL MOVING OBJECTS HAVE WAVELENGTHS EVEN

EVERYDAY OBJECTS, HOWEVER LARGE MASS PARTICLES EXHIBIT VERY SHORT WAVELENGTHS.

FOR EXAMPLE: WHAT IS THE WAVELENGTH OF A 60 Kg RUNNER WHO IS MOVING AT 10 METERS / SECOND?

= h / m x v, = (6.63 x10-34) / (60 x 10)

= 1.11 x 10-36 METERS

(A VERY, VERY SMALL WAVELENGTH)

PLANCK’S EQUATION AND ELECTRON ENERGIES• WHEN LIGHT IS EMITTED BY ENERGIZED ATOMS IT CAN

BE SEPARATED INTO ITS COMPONENT WAVELENGTHS AND FREQUENCIES. THESE FREQUENCIES ARE CONVERTED TO ENERGIES USING PLANCK’S EQUATION.

• FROM THIS DATA THE ENERGY STATE OF ELECTRONS WITHIN THE ATOM CAN BE DETERMINED !

• USING THIS INFORMATION, AN ENERGY LEVEL DIAGRAM FOR ELECTRONS CAN BE CONSTRUCTED.

Energized Hydrogen gas

Prism

Component wavelengths

ENERGY LEVEL DIAGRAM FOR ELECTRON STRUCTURE OF ATOMS

• CALCULATIONS REGARDING ELECTRON ENERGIES RESULTED IN THE DISCOVERY OF QUANTUM NUMBERS WHICH LEAD TO ENERGY LEVELS (SHELLS), ATOMIC ORBITALS (SUBSHELLS) AND ELECTRON POPULATION OF ATOMS

• ENERGY LEVELS ARE ENERGY STATES WITHIN ATOMS WERE ELECTRONS HAVE A HIGH PROBABILITY OF BEING FOUND

• ORBITALS ARE ENERGY STATES THAT EXIST AT THE ENERGY LEVELS WHERE ELECTRONS CAN BE LOCATED.

• ENERGY LEVELS ARE DESIGNATE BY INTEGERS BEGINNING AT 1 (THE LOWEST ENERGY STATE) AND RANGE UPWARD THROUGH 2, 3, 4, ETC.

• ORBITALS ARE DESIGNATED BY LETTERS, S, p, d AND f.

ENERGY LEVEL DIAGRAM FOR ELECTRON STRUCTURE OF ATOMS (CONT’D)

• IT HAS BEEN DETERMINED THAT ORBITALS ARE ARRANGED AT EACH ENERGY LEVEL IN A VERY SPECIFIC PATTERN.

• N IS USED TO REPRESENT ENERGY LEVELS

• AT ENERGY LEVEL 1 (n = 1), ONLY AN S ORBITAL OCCURS

• AT ENERGY LEVEL 2 (n = 2), S & p ORBITALS OCCUR

• AT ENERGY LEVEL 3 (n = 3), S, p & d ORBITALS OCCUR

• AT ENERGY LEVEL 4 (n = 4), S, p, d & f ORBITALS OCCUR

ENERGY LEVEL DIAGRAM FOR ELECTRON STRUCTURE OF ATOMS (CONT’D)

• ORBITALS OF EACH TYPE OCCUR IN DIFFERENT GROUPINGS. S ORBITAL OCCUR ONLY AS SINGLE ORBITALS WHILE p ORBITALS OCCURS AS A GROUP OF THREE, d ORBITALS IN FIVES AND f ORBITALS IN SEVENS.

• ORBITAL TYPE NUMBER OF ORBITALS MAX. # e- *

s 1 2

p 3 6

d 5 10

f 7 14

*EACH ORBITAL CAN CONTAIN A MAXIMUM OF 2 ELECTRONS HOWEVER ORBITALS MAY HAVE NO ELECTRONS OR BE HALF FILLED WITH ONE ELECTRON.

ENERGY LEVEL DIAGRAM FOR ELECTRON STRUCTURE OF ATOMS (CONT’D)

• USING THE INFORMATION PROVIDED BY QUANTUM MECHANICS, THE SHAPES EACH TYPE OF ATOMIC ORBITAL WITHIN THE ATOM HAS BEEN DESCRIBED.

ENERGY LEVEL DIAGRAM FOR ELECTRON STRUCTURE OF ATOMS (CONT’D)

• IN ADDITION TO ENERGY STATES AND ORBITAL SHAPES, A COMPLETE ENERGY LEVEL DIAGRAM FOR THE ATOM HAS BEEN DETERMINED USING QUANTUM MECHANICAL DATA.

• THIS DIAGRAM IS USED TO PREDICT THE ELECTRONIC CONFIGURATIONS OF ATOMS

SUMMARY• ATOMS ARE COMPOSED OF A NUCLEUS AND EXTERNAL

ELECTRONS• THE ATOMIC NUMBERS ALLOWS US TO DETERMINE THE

NUMBER OF PROTONS AND ELECTRONS IN AN ATOM• THE ATOMIC MASS ALLOWS US TO DETERMINE THE NUMBER

OF NEUTRONS IN THE MOST COMMON ISOTOPE OF AN ELEMENT

• ELECTRONS HAVE BOTH WAVE AND PARTICLE NATURES• THE PROPERTIES OF WAVES INCLUDE WAVELENGTH,

FREQUENCY AND SPEED

• THE EQUATION: x = c RELATES THE THREE PROPERTIES

• LIGHT ENERGY IN THE FORM OF PHOTONS CAN BE CALCULATED BY PLANCK’S EQUATION: E = h x

• ANALYZING LIGHT EMITTED BY ATOMS CAN ALLOW US TO DETERMINE THE ELECTRONIC STRUCTURE OF THE ATOM

SUMMARY (CONT’D)

• QUANTUM MECHANICS TELLS US THAT ELECTRONS ARE FOUND AT ENERGY LEVELS IN ORBITALS WITHIN THE ATOM

• ENERGY LEVELS AND ORBITALS ARE SETUP IN A VERY SPECIFIC MANNER IN THE ATOM

• ATOMIC ORBITALS INCLUDE S, p, d, AND f ORBITALS. EACH IS A DIFFERENT SHAPE AND CAN ACCOMMODATE DIFFERENT NUMBERS OF ELECTRONS

• AN ENERGY LEVEL DIAGRAM FOR ATOMS CAN BE OBTAINED FROM QUANTUM MECHANICS AND IT ALLOWS US TO ACCURATELY DESCRIBE THE ELECTRONIC STRUCTURE OF ATOMS

SUMMARY (CONT’S)

• OUR NEXT PROGRAM WILL SHOW HOW TO USE THE ENERGY LEVEL DIAGRAM FOR VARIOUS ATOMS AND IONS.

• TG