# 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

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
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

tektonikafrs
$N={N}_{0}{e}^{-\lambda t}$
${N}_{0}=$ Initial amount of sample = 44 gram
N = Final amount at time 't'
$5=44{e}^{-\lambda ×39.2}\phantom{\rule{0ex}{0ex}}⇒\frac{5}{44}={e}^{-\lambda ×39.2}\phantom{\rule{0ex}{0ex}}⇒\mathrm{ln}\left(0.1136\right)=\mathrm{ln}{e}^{\lambda ×39.2}\phantom{\rule{0ex}{0ex}}⇒-2.175=-\lambda ×39.2\phantom{\rule{0ex}{0ex}}⇒\lambda =\frac{-2.175}{-39.2}=0.055$
Half life of element $=\frac{\mathrm{ln}2}{\lambda }=\frac{\mathrm{ln}2}{0.055}$
Half life = 12.6 hours