- WELCOME TO NUCLEAR CHEMISTRY PART THREE.
NOW THAT WE'RE FAMILIAR
WITH THE DIFFERENT TYPES OF RADIOACTIVE DECAY,
IT'S AN IMPORTANT TO LEARN ABOUT HALF-LIVES
BECAUSE NOT EVERYTHING DECAYS AT THE SAME RATE.
LET'S GET STARTED. ALL RIGHT.
SO THE HALF-LIFE IS A VERY LITERAL TERM, RIGHT?
IT'S THE TIME FOR ONE-HALF OF THE SAMPLE TO DECAY.
ALL RIGHT. OKAY.
WE'LL SEE-- OH, WE'LL GO TO ONE-HALF OF ITS
ORIGINAL MASS.
ALL RIGHT. I GUESS IT'D BE--
I THINK I MIXED--
ALL RIGHT.
TIME FOR THE SAMPLE TO DECAY TO ONE-HALF IT'S ORIGINAL MASS.
WE'LL GO WITH THAT. OKAY.
SO T 1/2, THE HALF-LIFE.
ALL RIGHT.
SO LET'S LOOK AT A CHART HERE.
SO HERE WE HAVE THE MASS OF IODINE, 131 IN MILLIGRAMS,
AND SO WE SEE THAT WE STARTED WITH 80 MILLIGRAMS
OF IODINE 131.
NOW, AS WE LOOK, EIGHT DAYS LATER,
NOTICE NOW WE HAVE ONE-HALF OF THE ORIGINAL SAMPLE.
SO, IF WE LOOK HERE, RIGHT, SO THERE WE GO.
SO, THERE'S THE FIRST HALF-LIFE.
OKAY. SO, IT TOOK US EIGHT DAYS--
RIGHT, THE 80 MILLIGRAMS SAMPLE,
IT TOOK IT EIGHT DAYS TO GET TO 40 MILLIGRAMS.
NOW, IF WE WAIT ANOTHER EIGHT DAYS
NOW WE'RE DOWN TO 20 MILLIGRAMS.
SO NOTICE HERE, RIGHT, SO FROM HERE TO HERE,
THIS WAS THE SECOND HALF-LIFE.
RIGHT, SO HERE WE GO.
THIS WAS T 1/2 AND THEN HERE WAS THE FIRST HALF-LIFE. OKAY.
AND THEN LAST BUT NOT THE LEAST,
WE'LL LOOK HERE AND WE CAN GET ALL THE WAY DOWN TO 10.
AND SO ONCE AGAIN WE'VE WAITED ANOTHER EIGHT DAYS,
AND SO NOW IN THE THIRD HALF-LIFE
THE SAMPLE DROPS FROM 20 MILLIGRAMS TO 10 MILLIGRAMS.
SO NOTICE THAT THERE'S LESS AND LESS SAMPLE,
THERE'S LESS TO LOSE BUT THE HALF-LIVES
ALWAYS REMAIN THE SAME.
ALL RIGHT.
SO, NOW, LET'S LOOK AT SOME DIFFERENT RADIO ISOTOPES
AND COMPARE THEIR HALF-LIVES.
SO WE'LL LOOK ON THE NEXT PAGE.
AND WE CAN SEE THAT HALF-LIVES ARE INDEPENDENT OF THE TYPE
OF RADIOACTIVE DECAY, RIGHT.
SO WE CAN SEE HERE SOME GAMMA EMITTERS,
BARIUM 131, RIGHT A LITTLE OVER 11 DAYS.
AND THEN HERE'S COBALT 60, FIVE YEARS OVER FIVE YEARS.
URANIUM, YOU KNOW, TEN TO THE NINTH YEARS, RIGHT.
SO THERE'S NO RELATIONSHIP BETWEEN THE TYPE
OF RADIATION AND THE HALF-LIFE.
SO ALPHA, BETA, GAMMA,
POSITRON EMITTERS, THEY--
IT DEPENDS ON THE NUCLEUS,
THEY CAN HAVE SHORT OR VERY LONG HALF-LIVES
AND THERE'S NO RELATIONSHIP THERE.
ALL RIGHT.
SO LET'S PRACTICE. LET'S SEE HERE.
SO LET'S CONSIDER THAT WE HAVE A HUNDRED GRAM SAMPLE
OF CHROMIUM 151.
RIGHT, SO THERE'S CHROMIUM 151 RIGHT THERE.
WE SEE, RIGHT, THAT IT HAS A HALF-LIFE OF 27.8 DAYS.
SO, HOW LONG WOULD IT TAKE HALF OF THE SAMPLE TO DECAY?
VERY SIMPLE, 27.8 DAYS.
HOW MANY GRAMS OF CHROMIUM 51 WILL REMAIN AFTER 83.4 DAYS?
SO, THE TRICK HERE IS THAT WE HAVE TO FIGURE OUT
HOW MANY HALF-LIVES. ALL RIGHT.
SO I WILL ALWAYS GIVE YOU WHOLE NUMBER HALF-LIVES.
SO, RIGHT--
SO WE NEED THE NUMBER OF HALF-LIVES.
RIGHT, SO WE TAKE THE TIME AND DIVIDE IT BY THE HALF-LIFE.
SO IF WE HAVE 83.4 AND WE DIVIDE THAT BY 27.8 DAYS,
OKAY, THEN I'M GUESSING THIS SHOULD COME OUT--
HMM, I DON'T HAVE THIS--
SO I WILL DO IT ON THE SIDE.
SO, IT'S GOT TO BE THREE, I WOULD THINK.
YEAH. OKAY.
SO, WE WOULD GET THREE HALF-LIVES.
ALL RIGHT. SO, NOW,
WE CAN ESTIMATE OF THE HUNDRED GRAMS OF CHROMIUM, RIGHT?
SO WE STARTED WITH A HUNDRED GRAMS,
AND AFTER THE FIRST HALF-LIFE WE WILL HAVE FIFTY GRAMS.
AFTER THE SECOND HALF-LIFE WE WILL HAVE 25 GRAMS,
AND AFTER THE THIRD HALF-LIFE WE WILL HAVE 12.5 GRAMS
OF CHROMIUM 51. THERE WE GO. ALL RIGHTY.
SO THE MAIN THING IS TO--
AND THINK ABOUT THE CHART ON THE PREVIOUS PAGE, RIGHT.
SO WE DETERMINED THAT THERE ARE THREE HALF-LIVES,
WITH EACH HALF-LIFE WE LOSE HALF OUR SAMPLE.
SO 50, 25, 12 1/2. ALL RIGHTY.
NOW, LET'S LOOK AT THIS NEXT QUESTION.
CONSIDERING ONLY THE HALF-LIVES OF--
LET'S SEE.
WE'LL DO THE CARBON 14
AND BARIUM 131. OKAY.
SO LET'S GO BACK UP TO OUR CHART. OKAY.
SO, WE'RE ONLY GOING TO COMPARE THE HALF-LIVES.
ALL RIGHT. SO WE HAVE ONE THAT'S IN DAYS,
AND ONE THAT'S IN YEARS.
WHICH WOULD BE MORE APPROPRIATE
FOR INTERNAL USE IN A MEDICAL TEST?
WELL, IT WOULD DEFINITELY BE THE BARIUM 131
BECAUSE THE HALF-LIFE IS ONLY 11.6 DAYS.
SO, IF THE PATIENT WAS TO RECEIVE A MEDICAL--
A NUCLEAR MEDICINE TREATMENT,
RIGHT, WITHIN ABOUT FOUR OR FIVE HALF-LIVES WITHIN SIXTY DAYS,
ALL OF THE BARIUM 131 WILL HAVE DECAYED AND THE PATIENT
WILL NO LONGER BE EXPOSED, RIGHT?
CARBON 14, WITH IT'S 5730 YEAR HALF-LIFE,
RIGHT, THIS IS TOO LONG.
RIGHT, THERE'D BE TOO MUCH--
THERE'S TOO MUCH EXPOSURE TO THE PATIENT.
ALL RIGHT.
FOR MEDICAL USE. OKAY.
NOW, LET'S LOOK HERE.
ALL RIGHTY.
SO, WHAT PERCENT OF CARBON 14
REMAINS IN A SAMPLE ESTIMATED TO BE 17,000 YEARS OLD? ALL RIGHTY.
WELL, ONCE AGAIN, WE LOOK AT THE NUMBER OF HALF-LIVES,
ALL RIGHT, SO HERE'S THE TIME DIVIDED BY THE HALF-LIFE,
AND ONCE AGAIN WE SEE THAT WE HAVE ABOUT THREE HALF-LIVES.
ALL RIGHT.
SO HERE, WE'LL JUST GO IN TERMS OF PERCENTAGES, RIGHT.
SO WE HAVE A HUNDRED PERCENT OF THE SAMPLE.
SO, AFTER THE FIRST HALF-LIFE WE WOULD HAVE 50%,
AFTER THE SECOND HALF-LIFE WE WOULD HAVE 25%,
AND AFTER THE THIRD HALF-LIFE WE'RE BACK DOWN
TO THE 12 AND A HALF PERCENT.
SO, ONCE AGAIN--
SO YOU START TO GET USED TO WHEN YOU'RE WORKING WITH--
WHEN YOU'RE WORKING WITH HALF-LIVES IN CALCULATIONS,
YOU JUST WANT TO KEEP THINKING IN TERMS OF A HALF,
AND THEN ANOTHER HALF, AND THEN ANOTHER HALF.
SO YOU WANT TO THINK IN TERMS OF QUARTERS, AND EIGHTHS,
AND THEN SIXTEENTHS,
AND THIRTY-SECONDS, RIGHT.
SO, THEN YOU WANT TO THINK IN TERMS OF MULTIPLES,
RIGHT, ONE OVER TWO TO THE N. SO THINK IN TERMS
OF THE POWERS OF TWO,
AND THEN YOU WANT TO BE ABLE
TO CONVERT THESE TWO PERCENTAGES, RIGHT.
SO ANYTIME WE HAVE A HALF,
THINK FIFTY PERCENT, RIGHT.
QUARTER, THINK TWENTY-FIVE.
EIGHTH, TWELVE AND A HALF, RIGHT.
THEN WE GET DOWN HERE, 6 1/4, 3 3/4.
RIGHT, SO, AND AS FAR AS MATH SKILLS,
AS LONG AS YOU CAN DO YOUR EXPONENTS OF TWO
AND CONVERT TWO PERCENTAGES,
YOU'RE GOING TO BE IN GOOD SHAPE.
ALL RIGHT.
NOW LET'S LOOK AT THE LAST PAGE
HERE FOR THIS PART OF THE SERIES.
AND LET'S SEE WHAT'S GOING ON HERE.
OKAY. SHOWN BELOW IS A PORTION
OF A DECAY SERIES FOR PLUTONIUM 231-- EXCUSE ME,
241. THE SERIES HAS TWO KINDS OF ARROWS,
SHORTER ARROWS POINTING TO THE RIGHT,
LONGER ARROWS POINTING TO THE LEFT.
LABEL THE ARROWS TO INDICATE THE TYPE
OF NUCLEAR DECAY THAT IS OCCURRING,
AND THEN GIVE THE ELEMENTAL SYMBOL FOR Z
AND A TO INDICATE THE RESULTING ISOTOPE
OF THE DECAY SERIES, RIGHT.
SO WHERE DID WE START?
WE STARTED AT PLUTONIUM 241
AND THEN WE NOTICE, RIGHT,
THAT IT GOES--
ALL RIGHT.
SO THE SAME, THERE'S OUR ATOMIC NUMBER, RIGHT.
IT WOULD BE 94, AND THEN WHAT WE'LL DO?
WE WENT TO 95. SO,
WHAT THEN CAN WE SEE?
WE SEE THAT A NEUTRON BECAME A PROTON
AND WE LOST A BETA PARTICLE, RIGHT.
SO THERE IS OUR BETA DECAY.
OKAY. SO WHAT ISOTOPE,
LET ME SEE. ALL RIGHTY.
AND SO, I GUESS THAT WOULD MAKE--
YEAH, THAT WOULD MAKE A NEPTUNIUM 241, OKAY.
NOW WE LOOK AND WE SEE THAT WE HAVE A LOSE HERE.
RIGHT, WE HAVE A LOSE OF THE MASS NUMBER. OH, OKAY.
AND THERE WE GO FROM 95 TO 93.
HUH, THAT'S--
THAT SEEMS WEIRD TO ME BUT WE'LL JUST KEEP GOING.
THERE'S OUR ALPHA AND THEN WE HAVE ANOTHER ALPHA.
OH, I SEE.
I MADE A MISTAKE. ALL RIGHT.
I PUT THE AXIS HERE, AND I DIDN'T DO A GOOD JOB.
SO, YEAH, WE'RE GOING TO HAVE TO IGNORE THESE.
SORRY ABOUT THAT. ALL RIGHTY.
SO THEN THIS WOULD BE HERE.
THIS WOULD BE RIGHT, TWO-THIRTY-SEVEN,
AND THAT WOULD BE MINUS TWO TWO-THIRTY-NINE.
OOPS, 39. OKAY.
WE'LL JUST KEEP GOING.
AND THEN THE LAST PART HERE IS THEN WE WOULD HAVE THE BETA.
ALL RIGHTY. SO, WHAT DO WE END UP WITH THEN?
WELL, THE Z IS 292, YEAH, SO THIS WOULD BE URANIUM IS 92,
AND WE WOULD END UP WITH 233 FOR THE MASS NUMBER.
SO THAT IS THE ANSWER TO WRITE THE ELEMENT THAT--
IS AT THE END OF THE DECAY SERIES.
ALL RIGHTY.
NOW, LET'S LOOK AT THIS LAST ONE HERE FOR PRACTICE.
WHAT IS THE HALF-LIFE OF A RADIONUCLIDE
WITH THE FOLLOWING DECAY CURVE RIGHT,
SO HERE'S THE SAMPLE REMAINING.
SO, REMEMBER THE KEY HERE IS TO LOOK--
WE STARTED AT A 100%, SO WE WANT TO GET TO 50.
SO, IF WE LOOK HERE, RIGHT,
WE FIND 50% AND THEN WE LOOK DOWN,
AND WE SEE THIS IS THE TIME AND YEARS, SO,
THE HALF-LIFE WOULD BE APPROXIMATELY FOUR YEARS.
ALL RIGHTY.
SO, THAT PRETTY MUCH CONCLUDES WHAT THE KIND OF QUESTIONS
THAT WE COULD ASK ABOUT HALF-LIFE, RIGHT.
HOW MUCH SAMPLE IS LEFT, TO FIGURING OUT
THE TOTAL NUMBER OF HALF-LIVES, AND THAT SORT OF THING.
PLEASE TAKE SOME TIME NOW TO WORK A FEW HOMEWORK PROBLEMS
TO REINFORCE YOUR UNDERSTANDING.