Question

Certain radioactive material decays at a rate proportional to the amount present. If you currently have 300 gr of the material and after 2 years it is observed that 14% of the original mass has disintegrated, find:

a) An expression for the quantity of material at time t.

b) The time necessary for 30 percent to have disintegrated.

Answer #1

A radioactive material disintegrates at a rate proportional to
the amount currently present. If Q(t) is the amount present at time
t, then
dQ/dt =−rQ
where r>0 is the decay rate.
If 100 mg of a mystery substance decays to 81.14 mg in 4 weeks,
find the time required for the substance to decay to one-half its
original amount. Round the answer to 3 decimal places.
______________weeks

A sample of a certain radioactive material decays to 89.36% of
its mass after 2 years.
a. What is the half-life of the material? Show your calculations
and keep four significant figures of accuracy.
b. How long would it take for the sample to decay to 10% of its
original mass? How much longer after that would it take to decay to
1% of its original mass?

strontium 90 is a radioactive material that decays
according to the function A(t)=Aoe^0.0244t ,where So is the initial
amount present and A is the amount present at time t (in year).
assume that a scientist has a sample of 800 grams of strontium
90.
a)what is the decay rate of strontium 90?
b)how much strontium 90 is left after 10 years?
c)when Will only 600 grams of strontium 90 be left?
d)what is the half life of strontium 90?

An exponential decay function can be used to model the number of
grams of a radioactive material that remain after a period of
time. Carbon-14 decays over time, with the amount remaining after
t years given by y=y 0 e Superscript negative 0.00012378
ty=y0e−0.00012378t, where y0 is the original amount. If the
original amount of carbon-14 is 450450 grams, find the number of
years until 346346 grams of carbon-14 remain.

At
the beginning of an experiment, 142 grams of a radioactive chemical
were present in the sample of soil. After 24.5 hours, 10.5% of the
quantity was gone. If the rate of decay is proportional to the
amount present at time t, find the amount remaining after 48
hours.

Initially 100 milligrams of a radioactive substance was present.
After 5 hours the mass had decreased by 7%. If the rate of decay is
proportional to the amount of substance present at time t,
determine the half-life of the radioactive substance

Initially 100 milligrams of a radioactive substance was present.
After 8 hours the mass had decreased by 4%. If the rate of decay is
proportional to the amount of the substance present at time
t, determine the half-life of the radioactive substance.
(Round your answer to one decimal place.)

Carbon-14 is a radioactive isotope used to date objects. If A0
represents the initial amount of carbon-14 in the object, then the
quantity remaining at time t, in years, is A(t) = A0e^−0.000121t
.
(a) A tree, originally containing 185 micrograms of carbon-14,
is now 500 years old. At what rate is the carbon-14 decaying
now?
(b) In 1988, scientists found that the Shroud of Turin, which
was reputed to be the burial cloth of Jesus, contained 91% of the...

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that it first undergoes an alpha decay followed by a beta decay.
During the alpha decay Q1 energy is released, and during the beta
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final product after these two decays in terms of the released
energies, the mass of the parent nucleus, and the decay products.
For your physical representation you should draw diagrams of the
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The half-life of the radioactive material cesium-137 is 30
years. Suppose we have a 180-mg sample.
(a) Write a formula that gives the mass that remains after
t years. (Round the relative growth rate to four decimal
places.)
A(t) =
(b) How much of the sample remains after 100 years? (Round your
answer to two decimal places.)
mg
(c) After how long will only 1 mg remain? (Round your answer to one
decimal place.)
years
(d) At what rate is...

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