simot2omela
Answered

Uranium-232 has a half-life of 68.8 years. After 344.0 years, how much uranium-232 will remain from a 100.0-g sample?


1.56 g

3.13 g

5.00 g

20.0 g

Verified Answer :

mpanderla95

To solve this question first determine the number of half lives have gone by to equal 344 years. Which is 5 half lives. Then starting with 100 grams keep on multiplying by 1/2 or dividing by 2 to obtain the amount after 5 half lives have occurred. The amount that will remain from a 100.0 gram sample is 3.13 grams.

Answer:  3.13 g

Explanation:

Radioactive decay follows first order kinetics.

Half-life of uranium-232 = 68.8 years

\(\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{68.8}= 0.010072674 year^{-1}\)

\(N=N_o\times e^{-\lambda t}\)

N = amount left after time t

\(N_0\) = initial amount

\(\lambda\) = rate constant

t= time

\(N_0\) = 100 g, t= 344 years, \(\lambda=0.010072674 years^{-1}\)

\(N=100\times e^{- 0.010072674 years^{-1}\times 344 years}\)

N=3.13g


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