Question

If 10% of a radioactive material decays in 5 days then the amount of original material left after 15 days is about

Answer 1

This will help you mate

Answer 2

The amount of original material left after 15 days is about 77 grams

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

k = rate constant  = ?

t = time for decay  = 5 days

a = let initial amount of the reactant  = 100 g

x = amount decayed =$\frac{10}{100}\times 100=10g$

a - x = amount left after decay process  = 100 - 10 = 90g

Now put all the given values in above equation, we get

$5=\frac{2.303}{k}\log\frac{100}{90}$

$k=0.02days^{-1}$

Now to calculate the amount of original material left after 15 days

$15=\frac{2.303}{0.02}\log\frac{100}{(a-x)}$

$\log\frac{100}{(a-x)}=0.13$

$\frac{100}{(a-x)}=1.3$

$(a-x)=77g$

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