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Using Radioactive Decayto Date the IcemanWhen did this Iceman dic?Scientists answered this keyquestion by measuring thedegree of decay of the short-lived carbon isotope 1C inÖtzi's body. While most carbonatoms are the stable isotope12C.unstable radioactive isotope14C. created by cosmic raysbombarding nitrogen-14 (4N)atoms. This proportion of 14Cis captured by plants in pho-tosynthesis and is present inIn the fall of 1991. (wo Austrian hikers found a corpse stick-ing out of the melting snow on the crest of ahigh pass nearthe mountainous border between Italy and Austria. Rightaway it was clear the body was very old, frozen in anicynow released as the ice melted. Intiny proportion are theatrench long ago and onlythe years since this startling find, scientists have learned agreat deal about the dead man, whom they named Ötzi. Theyknow how old he was when he died, his health, the clothinghe wore, what he ate, and that he died from an arrow thatripped through his back. Its tip is still embedded in the backof his left shoulder. From the distribution of chemicals in histhe carbon molecules of the ani-teeth and bones, we know he lived his life within 60 km ofmal's body that eats the plant. Afterthe plant or animal dies, it no longeraccumulates any more carbon, and the1C present at the time of death decaysover time back to 14N. Gradually the ratioof 14C to 12C decreases. It takes 5730 yearsfor half of the 14C present to decay, alength of time called the half-life of the1C isotope. Because the half-life is aconstant that never changes, the extent ofradioactive decay allows the sample to bedated. Thus, a sample that had one-quarterof its original proportion of 14C remainingwould be approximately 11,460 years old(two half-lives).The graph displays the radioactivedecay curve of the carbon isotope 14C. Scien-tists know it takes 5730 years for half of the 14Cpresent in a sample to decay to nitrogen-14 (14N)When Ötzi's carbon isotopes were analyzed, researchersdetermined that the ratio of 14C to 12C, also written as thefraction 14C/12C, in Ötzi's body was 0.435 of the fractionfound in tissues of a person who has died recently.where he died.Radioactive Decay of Carbon Isotope 14C1--1.0001/21-0.5001/410OruC 0.2500.1251/8-11/161/320.0620.0310.00017,190 22,920 28,65011,4605,730Time (years)Analysisof the 14CApplying Concepts What proportionpresent in Otzi's body when he died is still theretoday? When he died, it would have been 1.0.2. Interpreting Data Plot this proportion on the 4Cradioactive decay curve above. How many half-livesdoes this point represent?3. Making Inferences If Otzi were indeed a recentcorpse, made to look old by the harsh weatherconditions found on the high mountain pass, whatwould you expect the ratio of 1C to 12C to be,relative to that in your own1.body?4. Drawing Conclusions When did Ötzi theIceman die?hoto Archives South Tyrol Museum of Archaeology -www.iceman.itPart I The Molecular Basis of LifeInquiry & AnalysisProportion of 14C remainingth Tyrel Museum of Archaeology-www.iceman.it

Question

#2

Using Radioactive Decay
to Date the Iceman
When did this Iceman dic?
Scientists answered this key
question by measuring the
degree of decay of the short-
lived carbon isotope 1C in
Ötzi's body. While most carbon
atoms are the stable isotope
12C.
unstable radioactive isotope
14C. created by cosmic rays
bombarding nitrogen-14 (4N)
atoms. This proportion of 14C
is captured by plants in pho-
tosynthesis and is present in
In the fall of 1991. (wo Austrian hikers found a corpse stick-
ing out of the melting snow on the crest of a
high pass near
the mountainous border between Italy and Austria. Right
away it was clear the body was very old, frozen in an
icy
now released as the ice melted. In
tiny proportion are the
a
trench long ago and only
the years since this startling find, scientists have learned a
great deal about the dead man, whom they named Ötzi. They
know how old he was when he died, his health, the clothing
he wore, what he ate, and that he died from an arrow that
ripped through his back. Its tip is still embedded in the back
of his left shoulder. From the distribution of chemicals in his
the carbon molecules of the ani-
teeth and bones, we know he lived his life within 60 km of
mal's body that eats the plant. After
the plant or animal dies, it no longer
accumulates any more carbon, and the
1C present at the time of death decays
over time back to 14N. Gradually the ratio
of 14C to 12C decreases. It takes 5730 years
for half of the 14C present to decay, a
length of time called the half-life of the
1C isotope. Because the half-life is a
constant that never changes, the extent of
radioactive decay allows the sample to be
dated. Thus, a sample that had one-quarter
of its original proportion of 14C remaining
would be approximately 11,460 years old
(two half-lives).
The graph displays the radioactive
decay curve of the carbon isotope 14C. Scien-
tists know it takes 5730 years for half of the 14C
present in a sample to decay to nitrogen-14 (14N)
When Ötzi's carbon isotopes were analyzed, researchers
determined that the ratio of 14C to 12C, also written as the
fraction 14C/12C, in Ötzi's body was 0.435 of the fraction
found in tissues of a person who has died recently.
where he died.
Radioactive Decay of Carbon Isotope 14C
1-
-1.000
1/21
-0.500
1/4
10
OruC 0.250
0.125
1/8-1
1/16
1/32
0.062
0.031
0.000
17,190 22,920 28,650
11,460
5,730
Time (years)
Analysis
of the 14C
Applying Concepts What proportion
present in Otzi's body when he died is still there
today? When he died, it would have been 1.0.
2. Interpreting Data Plot this proportion on the 4C
radioactive decay curve above. How many half-lives
does this point represent?
3. Making Inferences If Otzi were indeed a recent
corpse, made to look old by the harsh weather
conditions found on the high mountain pass, what
would you expect the ratio of 1C to 12C to be,
relative to that in your own
1.
body?
4. Drawing Conclusions When did Ötzi the
Iceman die?
hoto Archives South Tyrol Museum of Archaeology -www.iceman.it
Part I The Molecular Basis of Life
Inquiry & Analysis
Proportion of 14C remaining
th Tyrel Museum of Archaeology-www.iceman.it
help_outline

Image Transcriptionclose

Using Radioactive Decay to Date the Iceman When did this Iceman dic? Scientists answered this key question by measuring the degree of decay of the short- lived carbon isotope 1C in Ötzi's body. While most carbon atoms are the stable isotope 12C. unstable radioactive isotope 14C. created by cosmic rays bombarding nitrogen-14 (4N) atoms. This proportion of 14C is captured by plants in pho- tosynthesis and is present in In the fall of 1991. (wo Austrian hikers found a corpse stick- ing out of the melting snow on the crest of a high pass near the mountainous border between Italy and Austria. Right away it was clear the body was very old, frozen in an icy now released as the ice melted. In tiny proportion are the a trench long ago and only the years since this startling find, scientists have learned a great deal about the dead man, whom they named Ötzi. They know how old he was when he died, his health, the clothing he wore, what he ate, and that he died from an arrow that ripped through his back. Its tip is still embedded in the back of his left shoulder. From the distribution of chemicals in his the carbon molecules of the ani- teeth and bones, we know he lived his life within 60 km of mal's body that eats the plant. After the plant or animal dies, it no longer accumulates any more carbon, and the 1C present at the time of death decays over time back to 14N. Gradually the ratio of 14C to 12C decreases. It takes 5730 years for half of the 14C present to decay, a length of time called the half-life of the 1C isotope. Because the half-life is a constant that never changes, the extent of radioactive decay allows the sample to be dated. Thus, a sample that had one-quarter of its original proportion of 14C remaining would be approximately 11,460 years old (two half-lives). The graph displays the radioactive decay curve of the carbon isotope 14C. Scien- tists know it takes 5730 years for half of the 14C present in a sample to decay to nitrogen-14 (14N) When Ötzi's carbon isotopes were analyzed, researchers determined that the ratio of 14C to 12C, also written as the fraction 14C/12C, in Ötzi's body was 0.435 of the fraction found in tissues of a person who has died recently. where he died. Radioactive Decay of Carbon Isotope 14C 1- -1.000 1/21 -0.500 1/4 10 OruC 0.250 0.125 1/8-1 1/16 1/32 0.062 0.031 0.000 17,190 22,920 28,650 11,460 5,730 Time (years) Analysis of the 14C Applying Concepts What proportion present in Otzi's body when he died is still there today? When he died, it would have been 1.0. 2. Interpreting Data Plot this proportion on the 4C radioactive decay curve above. How many half-lives does this point represent? 3. Making Inferences If Otzi were indeed a recent corpse, made to look old by the harsh weather conditions found on the high mountain pass, what would you expect the ratio of 1C to 12C to be, relative to that in your own 1. body? 4. Drawing Conclusions When did Ötzi the Iceman die? hoto Archives South Tyrol Museum of Archaeology -www.iceman.it Part I The Molecular Basis of Life Inquiry & Analysis Proportion of 14C remaining th Tyrel Museum of Archaeology-www.iceman.it

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Step 1

In this context, it is given that, the half-life (t1/2) of the 14C isotope is 5730 years. The researcher mentioned that the proportion of 14C found in Otzi’s body was 0.435 of the fraction usually found in a dead person’s body.

Now, it is also mentioned that when Otzi died, the amount of 14C present in Otzi’s body was 1.

Step 2
Putting the values of the given information, in the given equation
N-N,
The N final amount of14C left = 0.435
No initial amount of14C 1
ti half-life of14C = 5730 years
t needs to be calculated
0.435 =1
3730
or, 0.435 0.530
taking log on both sides
log (0.435)3730
log 0.5
or, t 5730 log 0.435
log 0.5
or, t 6881.229
help_outline

Image Transcriptionclose

Putting the values of the given information, in the given equation N-N, The N final amount of14C left = 0.435 No initial amount of14C 1 ti half-life of14C = 5730 years t needs to be calculated 0.435 =1 3730 or, 0.435 0.530 taking log on both sides log (0.435)3730 log 0.5 or, t 5730 log 0.435 log 0.5 or, t 6881.229

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Step 3

It has been mentioned that Otzi’s body was found at the end of 1991, thus, till 2019, 28 years have passed.

 

So, the final t = 6881.29 + 28 years = 6909.29 years.

Thus, it can be concluded tha...

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