Problem: Lead-200 has a half-life of 21.50 hours. Starting with 3.770 mg of this isotope, how much would remain after 72.0 hours?a. 1.09b. 0.10c. 1.29d. 2.98e. 0.37

FREE Expert Solution

We’re being asked to determine the mass of Lead–200 remaining after 72.0 hours if there are 3.770 mg of Lead200 initially.


Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:


ln [N]t=-kt+ln [N]0


where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration


Also, recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half


The half-life of a first-order reaction is given by:


t12=ln 2k


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Problem Details

Lead-200 has a half-life of 21.50 hours. Starting with 3.770 mg of this isotope, how much would remain after 72.0 hours?

a. 1.09
b. 0.10
c. 1.29
d. 2.98
e. 0.37

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