"Annenberg Media" "¶" "WE HAVE, UP TO NOW," "STUDIED A SERIES OF EVENTS, IDEAS, AND DISCOVERIES" "WHICH HAVE GIVEN US A COHERENT VIEW" "OF HOW THE WORLD WORKS." "IT STARTED WITH COPERNICUS AND KEPLER AND GALILEO," "CULMINATING IN NEWTON'S THEORY OF MECHANICS." "THEN THERE WAS THE STUDY OF ELECTRICITY," "WHICH, IN TURN, CULMINATED WITH MAXWELL'S BEAUTIFUL THEORY." "BUT THERE TURNED OUT TO BE AN INNER CONTRADICTION" "BETWEEN THESE TWO GREAT SCIENCES." "MECHANICS IS BASED OF THE PRINCIPLE OF INERTIA," "WHICH MEANT THAT THERE COULD BE NO ABSOLUTE STATE OF REST." "AND THAT, IN TURN," "MEANS THAT THERE CAN BE NO ABSOLUTE SPEED." "BUT MAXWELL'S THEORY HADANABSOLUTESPEED" "THE SPEED OF LIGHT." "WELL, ALBERT EINSTEIN CAME ALONG" "AND RECONCILED THOSE IDEAS FOR US," "BUT WE HAD TO GIVE UP OUR INTUITIVE UNDERSTANDING" "OF THE MEANING OF SPACE AND TIME." "IN THE MEANTIME, A THIRD STORY WAS EVOLVING." "IT WAS THE STUDY OF MATTER." "IN A SENSE," "THERMODYNAMICS WAS PART OF THAT STORY," "BECAUSE IT DEALT WITH THE INTERACTIONS" "BETWEEN MATTER AND ENERGY." "AND IN THE END," "IT GAVE US A PROFOUND NEW VIEW" "OF THE MEANING OF THE FLOW OF TIME." "BUT THERE IS ONE ISSUE THAT WE HAVEN'T CONFRONTED YET" "THE AGE-OLD QUESTION" "OF THE ULTIMATE CONSTITUENTS OF MATTER." "BY THE TIME THAT QUESTION HAD BEEN ANSWERED," "EVERYTHING ELSE WE HAD LEARNED" "HAD BEEN TRANSFORMED PROFOUNDLY." "THAT ISSUE IS THE QUESTION BEFORE THE HOUSE TODAY." "IN THE SPRING OF 1913," "THE AGE-OLD QUESTION, "WHAT IS MATTER MADE OF?"" "WAS FRESH ON THE MIND OF NIELS HENRIK DAVID BOHR," "AND THE YOUNG DANE'S ANSWER," "FRESH TO THE POINT OF BEING REVOLUTIONARY," "WAS A MODEL OF THE HYDROGEN ATOM." "HIS WORK WAS PIVOTAL," "A TURNING POINT IN THEORETICAL PHYSICS." "BUT BY ALL THAT WAS HOLY IN THOSE DAYS" "NEWTON'S MECHANICS" "AND MAXWELL'S THEORY OF ELECTROMAGNETISM" "IT COULDN'T POSSIBLY BE RIGHT." "NONETHELESS, HIS IDEAS WERE BRILLIANTLY CONCEIVED." "IN THE FIRST PLACE," "BOHR ADOPTED A MODEL OF THE ATOM" "THAT RESEMBLED THE SOLAR SYSTEM IN MINIATURE." "A HEAVY POSITIVE NUCLEUS TOOK THE PLACE OF THE SUN," "AND LIKE A PLANET," "AN ELECTRON WAS SET INTO ORBIT AROUND IT." "BUT WHILE A PLANET IS ATTRACTED TO THE SUN" "BY THE FORCE OF GRAVITY," "THE ELECTRON IS ATTRACTED TO THE NUCLEUS" "BY THE FORCE OF ELECTRICITY." "SO IN SPITE OF THE DIFFERENCE BETWEEN THE TWO," "BOTH HAD FORCES" "OF THE SAME BASIC 1/r-SQUARED FORM," "AND BOTH WOULD HAVE THE SAME KINDS OF ORBITS." "AS JOHANNES KEPLER HAD OBSERVED" "AND ISAAC NEWTON HAD EXPLAINED CENTURIES EARLIER," "THOSE ORBITS WOULD BE ELLIPSES..." "OR, DEPENDING ON THEIR ECCENTRICITY," "POSSIBLY EVEN CIRCLES." "TO SIMPLIFY MATTERS," "NIELS BOHR ASSUMED ATOMS WOULD HAVE CIRCULAR ORBITS." "IN A CIRCULAR ORBIT, THE POTENTIAL ENERGY IS" "D/r." "THE KINETIC ENERGY IS POSITIVE," "BUT HALF AS BIG." "SO THE TOTAL ENERGY IS -1/2 D/r," "WHETHER FOR A PLANET OR FOR AN ATOM." "SINCE THIS SEEMED TO BE THE VERY MODEL" "OF A NEWTONIAN ATOM," "WHAT WAS THE MATTER WITH IT?" "IN OTHER WORDS," "HOW HAD THIS UPSTART VIOLATED THE PHYSICAL LAWS OF HIS DAY?" "AND IF HE REALLY HAD," "WHY DIDN'T ALL RIGHT-THINKING PHYSICISTS" "DISMISS HIS IDEAS ON THE SPOT?" "PERHAPS BECAUSE AT THIS POINT," "YOUNG BOHR WAS STILL ON SOLID GROUND," "WHICH MADE HIS WORK WORTH A SECOND GLANCE." "AND THAT'S WHEN THE PROBLEMS BECAME OBVIOUS." "BEING RADICAL, BOHR HAD GONE FURTHER," "FAR ENOUGH TO PROPOSE THAT AN ELECTRON COULD EXIST" "ONLY IN CERTAIN ORBITS," "WHICH WAS CONTRARY TO NEWTON'S LAWS." "THEN, CONTRARY TO MAXWELL," "BOHR SAID THE ELECTRON WOULD RADIATE OR ABSORB ENERGY" "ONLY WHEN IT JUMPED BETWEEN THESE DEFINITE ORBITS." "THOSE PROPOSALS WERE MORE THAN MERELY CONTRARY." "IN FACT, IN THE WORLD OF PHYSICS," "THEY WERE TOTALLY AGAINST THE LAW." "WHAT COULD POSSIBLY HAVE LED TO SUCH A TURN OF EVENTS?" "A GENERATION EARLIER," "WHEN IT CAME TO THE SUBJECT OF THE ATOM," "PROFESSOR JAMES CLERK MAXWELL QUITE LITERALLY WROTE THE BOOK." "AS AN EDITOR OF ENCYCLOPAEDIA BRITANNICA'S" "INCOMPARABLE NINTH EDITION," "HIS ENTRY ON THE ATOM WAS NOT ONLY" "THE MOST ADVANCED SCIENCE OF HIS DAY," "IT SUMMARIZED A BODY OF PHILOSOPHICAL SPECULATION" "THAT HAD BEEN AROUND SINCE THE GOLDEN AGE." "FOUR CENTURIES BEFORE CHRIST," "A GREEK PHILOSOPHER CALLED DEMOCRITUS" "SAW ATOMS AS SELF-PROPELLED PARTICLES" "MOVING THROUGH A VOID." "BUT ARISTOTLE DIDN'T SEE THINGS THE WAY DEMOCRITUS DID," "AND THUS, THE SUBJECT WAS CLOSED..." "UNTIL LATE IN THE RENAISSANCE," "WHEN GALILEO CAME ALONG TO REVIVE IT." "HE WAS FOLLOWED BY BOYLE, DESCARTES, NEWTON," "AND MANY SCIENTISTS ON THE SAME PATH," "INCLUDING MAXWELL." "IN MAXWELL'S OWN WORDS," ""IN MODERN TIMES, THE EXISTENCE OF ATOMS" "HAS ONCE MORE BECOME CONSPICUOUS AMONG SCIENTIFIC INQUIRIES."" "JOHN DALTON HAD MADE ONE OF THE MORE CONSPICUOUS INQUIRIES." "IN 1807, THIS ENGLISH CHEMIST" "STUDIED THE CHEMICAL COMBINATIONS" "OF THE COMMON ELEMENTS" "AND PROPOSED THE LAW" "OF SIMPLE AND MULTIPLE" "PROPORTIONS." "WHEN TWO SUBSTANCES" "COMBINE IN A CHEMICAL REACTION," "THEY'D COMBINE BY MASS IN RATIOS OF SMALL WHOLE NUMBERS." "THE IMPLICATION WAS CLEAR." "IN ORDER TO COMBINE INTO SUCH DEFINITE RATIOS," "SUBSTANCES MUST HAVE ULTIMATE PARTS, OR ATOMS." "DALTON'S IDEA WAS NOT WITHOUT DIFFICULTIES, HOWEVER," "AND ONE OF THE MOST IMPORTANT" "WAS SOLVED BY AN ITALIAN CHEMIST NAMED AMEDEO AVOGADRO." "FIRST, AVOGADRO REALIZED THAT EVEN THE SIMPLEST GASES," "SUCH AS PURE OXYGEN OR PURE NITROGEN," "WOULD BE COMPOSED NOT OF INDIVIDUAL ATOMS," "BUT OF COMBINATIONS OF ATOMS CALLED MOLECULES." ""WHATEVER THE SMALLEST UNIT OF ANY GAS," AVOGADRO SAID," "SPEAKING OF ATOMS OR MOLECULES," ""A GIVEN VOLUME OF GAS" "WOULD HAVE THE SAME NUMBER OF THEM."" "THAT QUANTITY EVENTUALLY BECAME KNOWN" "AS AVOGADRO'S NUMBER," "AND FINDING IT BECAME A VITAL STEP" "IN THE DEVELOPMENT OF ATOMIC THEORY." "IN MAXWELL'S WORDS," ""THE DIAMETER AND THE MASS OF A MOLECULE" ""ARE, OF COURSE, VERY SMALL," ""BUT BY NO MEANS INFINITELY SO." ""ABOUT TWO MILLIONS OF MOLECULES OF HYDROGEN IN A ROW" "WOULD OCCUPY A MILLIMETER."" "MAXWELL'S KNOWLEDGE CAME FROM THE THEORY OF GASES" "AND HIS ANALYSIS OF THEIR PROPERTIES," "THEIR VISCOSITY, THEIR ABILITY TO CONDUCT HEAT," "OR IN THIS CASE," "HOW LONG ONE KIND OF GAS ATOM" "TAKES TO MOVE A SPECIFIC DISTANCE" "THROUGH THE ATOMS OF ANOTHER GAS." "OBVIOUSLY, THAT WOULD DEPEND ON HOW FAST ATOMS MOVE," "ON HOW FAR APART THEY ARE," "AND ABOVE ALL," "ON THE SIZE OF EACH INDIVIDUAL ATOM OR MOLECULE." "TO THAT KNOWLEDGE-- THE SIZE OF AN ATOM" "MAXWELL COULD ADD NEW INSIGHTS THAT HAD BEEN GAINED" "FROM THE USE OF A NEW INSTRUMENT," "THE SPECTROSCOPE." "SPECTROSCOPES ARE USED TO ANALYZE LIGHT" "BY SEPARATING ITS VARIOUS COLORS OR FREQUENCIES." "WHEN ONE LOOKS AT A GAS OF ATOMS OF A SINGLE ELEMENT," "THE LIGHT SPECTRUM CONSISTS OF LINES" "AT CERTAIN FREQUENCIES," "A DIFFERENT SPECTRUM FOR EVERY ELEMENT." "AND THAT FACT WAS A CLUE" "INTO THE INNER NATURE OF THE ATOM." "IN MAXWELL'S WORDS," ""WHEN THE SPECTRUM CONSISTS OF A NUMBER OF BRIGHT LINES," ""THE MOTION OF THE SYSTEM MUST BE COMPOUNDED" "OF A CORRESPONDING NUMBER OF TYPES OF HARMONIC VIBRATION."" "IN OTHER WORDS," "ATOMS WOULD VIBRATE, LIKE A SIMPLE VIOLIN STRING," "AND EACH ATOM WOULD HAVE ITS OWN FREQUENCIES." "IF A MOLECULE WERE A SIMPLE VIBRATING MECHANICAL SYSTEM," "THEN THE FREQUENCIES OF THE BRIGHT LINES" "WOULD BE RELATED IN A RELATIVELY SIMPLE WAY." "MAXWELL HIMSELF DIDN'T EXPECT" "A SIMPLE RELATIONSHIP TO BE FOUND." "BUT IN 1885, A SWISS HIGH SCHOOL TEACHER," "JOHANN BALMER," "WROTE A FORMULA THAT NEARLY FIT THE WAVELENGTHS" "OF ALL THE KNOWN LINES IN THE SPECTRUM OF HYDROGEN." "SOON, THE SWEDISH MASTER OF THE SPECTROSCOPE," "JOHANNES RYDBERG," "GENERALIZED BALMER'S FORMULA." "IN RYDBERG'S VERSION," "A SERIES OF LINES WAS GENERATED BY EACH SET OF INTEGERS, m AND n," "AND THE QUANTITY R, CALLED THE RYDBERG CONSTANT," "WAS MEASURED WITH GREAT PRECISION." "FROM THAT POINT ONWARD," "IT WAS POSSIBLE TO PREDICT NEW LINES." "BUT TO UNDERSTAND THE NATURE OF THE ATOM" "IN A DEEPER SENSE" "WOULD REQUIRE SOMEONE TO MAKE A DISCOVERY" "ALONG DIFFERENT LINES." "THAT SOMEONE WAS PROFESSOR J.J. THOMSON," "A DISCIPLE OF MAXWELL" "IN THE THEORY OF ELECTROMAGNETISM," "A MAN DETERMINED TO LOOK INTO" "THE INTERNAL NATURE OF THE ATOM" "AND TO DISCOVER HOW IT WORKED." "OTHERS WOULD LATER TURN THE CATHODE-RAY TUBE" "INTO TV AND COMPUTER SCREENS." "BUT MORE SIGNIFICANT IN THE LONG RUN," "THOMSON'S EXPERIMENTS SHOWED" "THAT THE RAYS EMANATING FROM A HEATED CATHODE" "IN AN EVACUATED GLASS TUBE" "WERE ELECTRICALLY CHARGED PARTICLES." "THOSE RAYS COULD BE DEFLECTED BY ELECTRIC AND MAGNETIC FIELDS," "AND NO MATTER WHAT MATTER WAS IN THE TUBE," "THEY WERE ALWAYS THE SAME CHARGED PARTICLES." "THOMSON SAW THAT ALL ATOMS" "CONTAINED THE SAME WORKING PARTS," "OR, IN HIS WORDS, CORPUSCLES," "WHICH WOULD BECOME KNOWN AS ELECTRONS." "WITH THOSE PARTS IN MIND," "HE DEVELOPED WHAT WAS CALLED THE PLUM-PUDDING MODEL." "AND MORE THAN AN INTELLECTUAL SNACK," "IT WAS A SUBSTANTIAL EXPLANATION" "FOR LINE SPECTRA OF THE ELEMENTS." "IN PROFESSOR THOMSON'S THEORY," "EACH ATOM CONSISTS OF A LARGE SPHERE" "OF POSITIVE ELECTRIC CHARGE" "WITH JUST ENOUGH NEGATIVE ELECTRONS INSIDE" "TO BALANCE THE TOTAL CHARGE AND TO MAKE IT NEUTRAL." "THIS SEEMED A SENSIBLE IDEA," "BUT IT WOULD SOON FAIL A CRUCIAL TEST." "WEAREABLE TOBREAKUP ATOMS" "INA GREATVARIETYOFWAYS ." "BARON ERNEST RUTHERFORD," "NOBEL LAUREATE AND PEER OF THE REALM." "HE'D COME FROM NEW ZEALAND" "TO STUDY PHYSICS AT CAMBRIDGE," "AND HE'D HAD THE OPPORTUNITY TO WORK THERE" "UNDER PROFESSOR THOMSON." "...ADEFINITELAW LIKEA RADIOACTIVEELEMENT." "AND BY THE TIME HE SPOKE THESE WORDS," "HE'D NOT ONLY LONG SUCCEEDED HIS MENTOR" "AS DIRECTOR OF THE CAVENDISH LABORATORY," "RUTHERFORD HAD BECOME HEADMASTER OF THE ATOM ITSELF." "...ANDHASGIVENUS A MUCH CLEARER UNDERSTANDING..." "EVEN BEFORE RUTHERFORD BEGAN HIS EXPERIMENTS," "IT HAD BEEN DISCOVERED" "THAT ATOMS COULD SPLIT THEMSELVES NATURALLY" "AND EMIT ALPHA-RAY RADIOACTIVITY." "SO WHEN HE AND HIS ASSOCIATES" "PASSED ALPHA RAYS THROUGH THIN METAL FOILS," "THEIR EXPERIMENTS WENT PRECISELY" "AS EVERYONE WOULD HAVE PREDICTED." "...NUCLEARCHEMISTRY." "THE RAYS SEEMED TO SLICE THROUGH THE METAL" "AS IF IT WERE A PUDDING," "WITH VERY LITTLE RESISTANCE," "AND WENT STRAIGHT ALONG THEIR COURSE" "WITH HARDLY ANY DEVIATION." "BUT ONE FINE DAY IN SCIENTIFIC HISTORY," "THEY NOTICED THE UNEXPECTED." ""THE MOST INCREDIBLE EVENT THAT HAS HAPPENED IN MY LIFE,"" "STATED RUTHERFORD AFTER THE FACT." ""IT WAS ALMOST AS INCREDIBLE" ""AS IF YOU FIRED A 15-INCH SHELL" ""AT A PIECE OF TISSUE PAPER" "AND IT CAME BACK AND HIT YOU."" "THE INCREDIBLE EVENT WAS THAT" "RATHER THAN WINGING THEIR WAY THROUGH THE FOIL," "SOME OF THE ALPHA RAYS BOUNCED BACK." "RUTHERFORD REALIZED THAT, CONTRARY TO THOMSON'S MODEL," "ALL THE POSITIVE CHARGE OF THE ATOM" "HAD TO BE CONCENTRATED WITHIN A TINY NUCLEUS." "THAT WAS BECAUSE, WITH ALL THE POSITIVE CHARGE" "CONCENTRATED IN A VERY SMALL REGION," "THE ELECTRIC FORCE NEARBY" "WOULD BE LARGE ENOUGH TO REPEL, OR AT LEAST DEFLECT," "AN ENERGETIC ALPHA PARTICLE IF ONE GOT CLOSE ENOUGH." "IN ADDITION," "IF THE NUCLEUS HAD MOST OF THE MASS OF THE ATOM," "IT COULD REPEL THE OCCASIONAL ALPHA PARTICLE" "WITHOUT RECOILING VERY MUCH." "THESE IDEAS LEAD RUTHERFORD, IN 1911," "TO PROPOSE A PLANETARY MODEL OF THE ATOM." "ACCORDING TO RUTHERFORD," "THE SOLAR SYSTEM AND THE INVISIBLE ATOM" "WERE ALMOST MIRROR IMAGES OF EACH OTHER." "BOTH OBEYED NEARLY IDENTICAL LAWS." "IN RUTHERFORD'S MODEL," "EACH ATOM HAD A HEAVY NUCLEUS THAT WAS POSITIVELY CHARGED." "HIS NUCLEUS WAS SURROUNDED" "BY LIGHT, NEGATIVELY-CHARGED ELECTRONS" "THAT ORBITED LIKE PLANETS AROUND THE SUN." "BUT WHILE THE PLANETS WERE BOUND TOGETHER" "BY THE FORCE OF GRAVITY," "THE ATOMS WERE HELD TOGETHER BY THE FORCE OF ELECTRICITY." "LIKE A GREEK GODDESS IN THE HEAVENS," "THIS WAS AN IDEA OF INCREDIBLE BEAUTY." "AND BY THE SAME TOKEN," "IT WAS TOO GOOD TO BE TRUE." "FOR ONE REASON, WHEN ELECTRONS ARE ACCELERATED," "THEY RADIATE ENERGY IN THE FORM OF ELECTROMAGNATIC WAVES." "BUT AN ELECTRON IN ORBIT" "WOULD BE CONSTANTLY ACCELERATING," "ALWAYS RADIATING ENERGY." "GOING ROUND AND ROUND," "THE ELECTRON WOULD FALL INTO SMALLER AND SMALLER ORBITS," "RADIATING NOT SPECTRAL LINES," "BUT A CONTINUOUS RAINBOW OF COLORS." "AND FINALLY, NECESSARILY," "IT WOULD COLLAPSE INTO THE NUCLEUS." "DR. RUTHERFORD HAD OBEYED THE LAWS OF NEWTON AND MAXWELL," "AND THOSE VERY LAWS WERE THE DOWNFALL" "OF HIS MODEL OF A PLANETARY ATOM." "WHAT WAS NEEDED WAS AN EVEN BOLDER STEP." "AND THE PATH WOULD BE LIGHTED" "BY A DISCOVERY ABOUT LIGHT" "THAT HAD BEEN MADE JUST A FEW YEARS EARLIER." "IN 1900," "A GERMAN PHYSICIST SHED LIGHT ON THE SPECTRUM EMITTED" "BY A HEATED SOLID BODY." "HIS NAME WAS MAX PLANCK." "HIS THEORY HELD THAT MATTER" "EMITTED ONLY DISCRETE AMOUNTS OF RADIATION," "WITH ENERGY, E," "PROPORTIONAL TO THE FREQUENCY OF LIGHT, f." "ONE AMAZING THING ABOUT DR. PLANCK'S THEORY" "WAS THE QUANTITY h," "WHICH BECAME A NEW FUNDAMENTAL CONSTANT OF NATURE" "CALLED PLANCK'S CONSTANT." "IT WAS AMAZING BECAUSE IN MAXWELL'S THEORY," "THE ENERGY OF LIGHT DEPENDS ON ITS INTENSITY," "NOT ITS FREQUENCY." "BUT PERHAPS THE MOST AMAZING THING OF ALL" "WAS THE FACT THAT YOUNG NIELS BOHR" "TOOK PLANCK'S FORMULA" "AND USED IT TO CREATE A MODEL OF THE HYDROGEN ATOM." "BOHR ASSUMED THAT THE ELECTRON" "OF RUTHERFORD'S MODEL OF THE ATOM" "COULD EXIST IN CERTAIN SPECIAL ORBITS" "WITHOUT RADIATING ENERGY." "HE WENT ON TO ASSUME THAT RADIATION," "AT THE FREQUENCY GIVEN BY PLANCK'S FORMULA," "WOULD BE EMITTED OR ABSORBED" "WHENEVER AN ELECTRON" "JUMPED FROM ONE OF THESE ORBITS" "TO ANOTHER." "BOHR COULDN'T SAY WHY" "SUCH SPECIAL ORBITS SHOULD EXIST," "BUT HE KNEW THAT WITHOUT THEM," "THERE'D BE NO HOPE OF EXPLAINING SPECTRAL LINES." "HE ALSO KNEW THAT IN ASSUMING THOSE SPECIAL ORBITS," "HE WAS STEPPING BEYOND THE PHYSICS" "OF NEWTON AND MAXWELL" "AND INTO THE UNKNOWN." "BUT THERE STILL WAS A PROBLEM." "WHAT WOULD DETERMINE THE SIZES OF THOSE SPECIAL ORBITS?" "HE TRIED VARIOUS IDEAS," "BUT THE ONE HE CHOSE AMOUNTED TO THIS" "EACH ORBIT WOULD HAVE A DIFFERENT ANGULAR MOMENTUM," "AND PLANCK'S CONSTANT JUST HAPPENS TO HAVE THE UNITS" "OF AN ANGULAR MOMENTUM." "COULD IT BE THAT THE ALLOWED ORBITS" "HAVE ANGULAR MOMENTA GIVEN BY PLANCK'S CONSTANT?" "WELL, ALMOST." "IN FACT, THE ANGULAR MOMENTA" "ARE MULTIPLES OF h/2-PI," "A COMBINATION GIVEN ITS OWN SYMBOL," "CALLED h-BAR." "SO, IN NIELS BOHR'S MODEL OF THE HYDROGEN ATOM," "THE LOWEST ORBIT HAS ANGULAR MOMENTUM-- h-BAR." "THE NEXT ORBIT HAS 2 h-BAR." "THE NEXT HAS 3 h-BAR." "AND, IN FACT, AN ALLOWED ORBIT EXISTS" "FOR ANY INTEGER TIMES h-BAR." "PUTTING THESE IDEAS TOGETHER," "THE SIZES OF THE ALLOWED ORBITS ARE EASY TO FIND." "THE RADIUS OF EACH ORBIT" "IS PROPORTIONAL TO THE SQUARE OF THE INTEGER n." "THE RADIUS OF THE LOWEST ORBIT, WITH n EQUAL TO 1," "WOULD THEN GIVE THE NATURAL SIZE OF A HYDROGEN ATOM" "IN TERMS OF THE FUNDAMENTAL CONSTANTS OF PHYSICS." "ITS VALUE TURNED OUT TO BE" "JUST ABOUT HALF AN ANGSTROM UNIT." "THIS NUMBER WAS SMALL," "BUT ITS VALUE IN PHYSICS WAS ENORMOUS BEYOND COMPARE." "PREVIOUSLY, THE SIZE OF AN ATOM" "COULD HAVE BEEN JUST ABOUT ANYTHING." "BUT NOW, IF BOHR'S BOLD ASSUMPTIONS WERE CORRECT," "THE SIZE OF AN ATOM" "COULD BE SEEN AS A COMBINATION" "OF THE FUNDAMENTAL CONSTANTS OF NATURE." "BUT FOR NIELS BOHR, THAT WAS ONLY THE BEGINNING." "HE WAS NOW PREPARED TO CALCULATE THE PRECISE FREQUENCIES" "OF THE LINES IN THE HYDROGEN SPECTRUM." "EACH FREQUENCY WOULD BE THE RESULT" "OF A QUANTUM JUMP." "THAT IS, THE ATOM WOULD EMIT OR ABSORB LIGHT" "ONLY WHEN THE ELECTRON JUMPED" "FROM ONE ALLOWED ORBIT TO ANOTHER." "THE ELEMENTS OF THE CALCULATION" "WERE ALL AT HAND," "READY TO BE PUT TOGETHER." "FIRST, THE SIZES" "OF THE ALLOWED ORBITS." "THEN, THE ENERGIES" "OF THE ALLOWED ORBITS." "AND FINALLY," "THE ENERGY OF A JUMP BETWEEN ORBITS." "WHEN THESE WERE PUT IN RYDBERG'S EQUATION," "OUT CAME A FORMULA FOR THE RYDBERG CONSTANT ITSELF." "ITS COMPONENTS WERE, ONCE AGAIN," "FUNDAMENTAL CONSTANTS" "OF PHYSICS." "AND WHEN THEY WERE ALL" "PUT TOGETHER," "THEY YIELDED A PREDICTION" "THAT COULD BE COMPARED TO EXPERIMENT." "THE AGREEMENT BETWEEN NIELS BOHR'S MODEL" "AND THE EXPERIMENTAL MEASUREMENT" "WAS NOTHING SHORT OF AMAZING." "LIKE NEWTON'S IDEA OF ACTION AT A DISTANCE," "BOHR'S MODEL OF THE HYDROGEN ATOM" "WAS ACCEPTED NOT BECAUSE IT WAS EASY TO GRASP" "OR COMFORTABLE TO LIVE WITH." "INSTEAD, LIKE NEWTON," "BOHR PROVIDED COMPELLING AGREEMENT WITH OBSERVATION" "THAT COULDN'T BE DENIED." "NOBODY KNEW WHY BOHR'S MODEL OF THE ATOM SHOULD WORK," "AND YET, THE BEST MINDS AGREED THAT IT DID WORK." "WHY?" "BECAUSE IN BOHR'S PHYSICS, LIKE NEWTON'S," "THERE'S AN AGREEMENT BETWEEN THEORY AND EXPERIMENT" "THAT IS, QUITE SIMPLY, TOO PRECISE TO IGNORE." "NIELS BOHR TOOK THE OLD PHYSICS," "AND WITH HIS PROFOUND INSIGHT INTO THE ATOM," "PROPELLED IT DIRECTLY INTO THE FUTURE." "THE QUEST FOR THE NATURE OF THE ATOM" "IS PARTICULARLY INTERESTING," "BECAUSE PEOPLE WERE TRYING TO EXPLAIN SOMETHING" "THAT THEY COULDN'T SEE" "AND WHICH OBEYED RULES THAT HADN'T EVEN BEEN FORMULATED YET." "THE REAL QUESTION IS," "HOW IS IT POSSIBLE TO DO SOMETHING LIKE THAT?" "WHERE DO YOU BEGIN?" "WHAT YOU NEED WHEN YOU'RE CONFRONTING A SET" "OF CONFUSING INFORMATION" "IS SOME IDEA THAT SORTS IT OUT" "AND EXPLAINS THE MOST IMPORTANT FEATURES." "IT MAY NOT EXPLAIN EVERYTHING," "BUT IT GETS THE KEY THINGS, THE KEY FEATURES." "AN IDEA LIKE THAT" "ACTUALLY HAS A DEFINITE NAME IN SCIENCE." "IT'S CALLED A MODEL." "EVERY ONCE IN A WHILE" "YOU GET AN IDEA THAT YOU LIKE SO MUCH" "THAT YOU THINK IT DOES MORE THAN JUST GET THE KEY FEATURES." "YOU GET AN IDEA THAT YOU THINK IS REALLY RIGHT." "WHEN THAT HAPPENS, IT'S GOT ANOTHER NAME." "THAT'S CALLED A THEORY." "ONCE YOU'VE FORMULATED YOUR MODEL" "OR YOUR THEORY," "THE NEXT STEP REALLY IS THE KIND OF THING" "THAT WE DO TEACH YOU HOW TO DO." "IT'S A LITTLE LIKE DOING A HOMEWORK PROBLEM." "YOU HAVE TO WORK OUT THE CONSEQUENCES OF YOUR MODEL" "OR YOUR THEORY." "YOU MUST GET THE RIGHT ANSWER," "RIGHT IN THE SENSE" "THAT IT IS INDEED WHAT YOUR MODEL PREDICTS." "THEN YOU'VE GOT TO DO SOMETHING" "THAT WE CAN'T TEACH YOU HOW TO DO" "YOU HAVE TO USE JUDGMENT," "BECAUSE, INEVITABLY, THE CONSEQUENSES" "OF YOUR MODEL OR YOUR THEORY" "WILL DISAGREE WITH SOME PIECE OF INFORMATION." "THE QUESTION IS, WHAT DO YOU DO ABOUT THAT?" "HOW IMPORTANT IS IT?" "WHAT IS THE REASON FOR IT?" "IS IT BECAUSE OF SOME APPROXIMATION YOU HAD TO MAKE" "IN ORDER TO WORK OUT THE CONSEQUENCES OF YOUR THEORY?" "OR IS IT BECAUSE THE EXPERIMENT WAS WRONG?" "OR IS IT THE CRUCIAL CLUE" "THAT SHOWS THAT YOUR IDEA WAS WRONG," "AND YOU MUST START OVER AGAIN?" "IF I WERE TEACHING YOU HOW TO PAINT," "I COULD TEACH YOU HOW TO MIX COLORS." "I COULD TEACH YOU THE RULES OF PERSPECTIVE." "I COULD TEACH YOU HOW TO CHOOSE A CANVAS" "AND PREPARE IT." "BUT I COULD NEVER TEACH YOU HOW TO IMAGINE AND CREATE" "A PAINTING LIKE THE MONA LISA." "IT'S EXACTLY THE SAME IN SCIENCE." "I CAN TEACH YOU THE FACTS OF SCIENCE." "I CAN TEACH YOU THE MECHANICAL RULES" "FOR HOW TO DO SCIENCE." "I CAN NEVER TEACH YOU" "TO HAVE THE IMAGINATION, THE CREATIVITY," "AND THE JUDGMENT," "AND ABOVE ALL," "THE RELENTLESS DEDICATION TO WORK" "THAT ALL GREAT SCIENTISTS ALWAYS HAVE." "IF YOU WANT TO BE A GREAT SCIENTIST," "THOSE ARE THE THINGS" "THAT YOU'LL HAVE TO SUPPLY FOR YOURSELF." 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