1. The radioactive isotope of lead, Pb-209, decays at a rate proportional to the
ID: 1720522 • Letter: 1
Question
1. The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 80% of the lead to decay? (Round your answer to two decimal places.)
2. Archaeologists used pieces of burned wood, or charcoal, found at the site to date prehistoric paintings and drawings on walls and ceilings of a cave in Lascaux, France. See the figure below. Use the information from the section to determine the appropriate age of a piece of burned wood, if it was found that 85% of the C-14 found in living trees of the same type had decayed. (Round your answer to the nearest hundred years.)
3a. A thermometer is removed from a room where the temperature is 70° F and is taken outside, where the air temperature is 30° F. After one-half minute the thermometer reads50° F. What is the reading of the thermometer at
t = 1 min?
(Round your answer to two decimal places.)
How long will it take for the thermometer to reach 35° F? (Round your answer to two decimal places.)
4.A thermometer is taken from an inside room to the outside, where the air temperature is 25° F. After 1 minute the thermometer reads 75° F, and after 5 minutes it reads 50°F. What is the initial temperature of the inside room? (Round your answer to two decimal places.)
5.Two large containers A and B of the same size are filled with different fluids. The fluids in containers A and B are maintained at 0° C and 100° C, respectively. A small metal bar, whose initial temperature is 100° C, is lowered into container A. After 1 minute the temperature of the bar is 90° C. After 2 minutes (since being lowered into container A) the bar is removed and instantly transferred into the other container. After 1 minute in container B the temperature of the bar rises 10°. How long, measured from the start of the entire process, will it take the bar to reach 99.9° C? (Round your answer to two decimal places. Assume the final temperature being asked for is reached while the bar is container B.)
6.A dead body was found within a closed room of a house where the temperature was a constant 69°F. At the time of discovery, the core temperature of the body was determined to be 90°F. One hour later a second measurement showed that the core temperature of the body was 85°F. Assume that the time of death corresponds to
t = 0
and that the core temperature at that time was 98.6°F. Determine how many hours elapsed before the body was found. (Round your answer to one decimal place.)
7.A large tank is filled to capacity with 700 gallons of pure water. Brine containing 4 pounds of salt per gallon is pumped into the tank at a rate of 7 gal/min. The well-mixed solution is pumped out at the same rate. Find the number
A(t)
of pounds of salt in the tank at time t.
8.A 20-volt electromotive force is applied to an LR-series circuit in which the inductance is 0.1 henry and the resistance is 80 ohms. Find the current
i(t)
if
i(0) = 0.
Determine the current as
t .
9.A 100-volt electromotive force is applied to an RC-series circuit in which the resistance is 200 ohms and the capacitance is
104 farad.
Find the charge
q(t)
on the capacitor if
q(0) = 0.
Find the current
i(t).
Explanation / Answer
Solved the first two problem, please split the question into multiple parts to get the remaining answers
Q1) Using the decay equation of the radioactive isotope
ln(Ao/At) = kt
t1/2 = ln2/k, k = ln2/3.3 hr^(-1)
Ao = 1 gm
At = 0.2 gm, plugging the values in the equation we get
ln(1/0.2) = ln2/3.3 * t
t = 3.3ln(5)/ln(2) = 7.662 hours
Q2) Using the decay equation of the radioactive isotope
ln(Ao/At) = kt
t1/2 = ln2/k, k = ln2/5730 yr^(-1)
Ao = x gm
At = 0.15x gm, plugging the values in the equation we get
ln(1/0.15) = ln2/5730 * t
t = 5730ln(6.666)/ln(2) = 15682.73 years
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