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Answer:
a)
b) 11.4mg of cesium-137 remains after 120 years.
c) 225.8 years.
Step-by-step explanation:
The following equation is used to calculate the amount of cesium-137:
In which Q(t) is the amount after t years, Q(0) is the initial amount, and r is the rate at which the amount decreses.
(a) Find the mass that remains after t years.
The half-life of cesium-137 is 30 years.
This means that Q(30) = 0.5Q(0). We apply this information to the equation to find the value of r.
Applying ln to both sides of the equality.
So
180-mg sample, so Q(0) = 180
(b) How much of the sample remains after 120 years?
This is Q(120).
11.4mg of cesium-137 remains after 120 years.
(c) After how long will only 1 mg remain?
This is t when Q(t) = 1. So
Applying ln to both sides
225.8 years.