There is a 44-gram sample of a certain element. If it takes 39.2 hours for 5 grams to be left. Determine the half-life of the element.Set up your equation with the values you determined in the table and using the half-life formula

Adison Rogers
2022-11-13
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tektonikafrs

Answered 2022-11-14
Author has **15** answers

$N={N}_{0}{e}^{-\lambda t}$

${N}_{0}=$ Initial amount of sample = 44 gram

N = Final amount at time 't'

$5=44{e}^{-\lambda \times 39.2}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{5}{44}={e}^{-\lambda \times 39.2}\phantom{\rule{0ex}{0ex}}\Rightarrow \mathrm{ln}(0.1136)=\mathrm{ln}{e}^{\lambda \times 39.2}\phantom{\rule{0ex}{0ex}}\Rightarrow -2.175=-\lambda \times 39.2\phantom{\rule{0ex}{0ex}}\Rightarrow \lambda =\frac{-2.175}{-39.2}=0.055$

Half life of element $=\frac{\mathrm{ln}2}{\lambda}=\frac{\mathrm{ln}2}{0.055}$

Half life = 12.6 hours

${N}_{0}=$ Initial amount of sample = 44 gram

N = Final amount at time 't'

$5=44{e}^{-\lambda \times 39.2}\phantom{\rule{0ex}{0ex}}\Rightarrow \frac{5}{44}={e}^{-\lambda \times 39.2}\phantom{\rule{0ex}{0ex}}\Rightarrow \mathrm{ln}(0.1136)=\mathrm{ln}{e}^{\lambda \times 39.2}\phantom{\rule{0ex}{0ex}}\Rightarrow -2.175=-\lambda \times 39.2\phantom{\rule{0ex}{0ex}}\Rightarrow \lambda =\frac{-2.175}{-39.2}=0.055$

Half life of element $=\frac{\mathrm{ln}2}{\lambda}=\frac{\mathrm{ln}2}{0.055}$

Half life = 12.6 hours

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