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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

Respuesta :

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

[tex]\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{68.8}= 0.010072674 year^{-1}[/tex]

[tex]N=N_o\times e^{-\lambda t}[/tex]

N = amount left after time t

[tex]N_0[/tex] = initial amount

[tex]\lambda[/tex] = rate constant

t= time

[tex]N_0[/tex] = 100 g, t= 344 years, [tex]\lambda=0.010072674 years^{-1}[/tex]

[tex]N=100\times e^{- 0.010072674 years^{-1}\times 344 years}[/tex]

N=3.13g


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