As a radioactive sample decays, the amount of radioactive material that remains

Question

As a radioactive sample decays, the amount of radioactive material that remains decreases, and the count rate decreases exponentially with time: N = NQe~2i. In this equation, what are the units of the decay constant lambda if t is in seconds? (Enter your answer in MapleTA syntax.) The half-life is defined as the time it takes for half the amount of radioactive material No present at t = 0 to decay (in other words the time t for which N(t) = 0.5 No ). Write the equation in MapleTA syntax for the half life in terms of X. Use lambda for the decay constant. If you need to use the natural logarithm function, the MapleTA syntax for it is ln(x) for the natural logarithm of the number x . You will use this equation in the lab to convert from lambda . which you will measure, to the half-life t1/2. NOTE: The numbers given below will be "randomized" for each student. As long as you stay logged on, they will not change. If you log off and then log on again, your numbers may well be different. If a material, like the short-lived radioactive source in the lab, has a half-life of 2.6 minutes, what do you expect X will be? Use MapleTA syntax to express the proper SI units. The numeric part of the answer must be accurate to better than 0.5%. How long would it take for there to be only 1 % of this material left? Use MapleTA syntax to express the proper SI units. The numeric part of the answer must be accurate to better than 0.5%.

Explanation / Answer

a) s^(-1)

b) so e^(-lambda t1/2 ) = 1/2

-lambda t1/2 = ln(1/2)

t1/2 = ln(2)/lambda

c) lambda = ln(2)/(2.6*60) = 4.44E-3 s^-1

d) 2^(-t/t1/2) = 0.01

2^(-t/(2.6*60))=0.01

t=1036.4 s

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