could someone please explain how do this differentail equation problem: The amou
ID: 3344757 • Letter: C
Question
could someone please explain how do this differentail equation problem:
The amount of radioactive carbon-14 in a ample is measured using a Geiger counter, which records each disintegration of an atom. Living tissue disintegrates at a rate of about 13.5 atoms per minute per gram of carbon. In 1977 a charcoal fragment found at Stonehenge, England, recorded 8.2 disintegrations per minute per gram of carbon. Assuming that the half life of carbon-14 is 5730 years and that the charcoal was formed during the building of the site, estimate the date at which Stonehenge was built.
Explanation / Answer
THE RATE OF DECAY IS PROPORTIONAL TO QTY OF MATERIAL PRESENT ..
DQ / DT = K*Q..DQ/Q=KDT
INTEGRATING
LN[Q]-LN[C]=KT
LN[Q/C]=KT
Q=C[E^(KT)]....................................................1
AT T=0......LET Q=13.5...................................2
P=13.5..................SO.................
Q=13.5*[E^(KT)]
Q=0.5*13.5 ...AT T= 5730 YEARS ...
0.5*13.5=13.5*[E^(K*5730)]
K=-0.0001209681
Q=13.5*[E^(-0.0001209681*T)]..........................................3
AT Q=8.2.....T=?..........................FROM EQN.3 , WE GET ....
T=4121.38 YEARS .......................ANSWER
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