Question

Half life time of 18F is 110 minutes. What fraction of 18F sample decays in 20 minutes?​

Answer 1

Answer:

360

Explanation:

we want multiple 18 × 20

Answer 2

The fraction of 18F sample decays in 20 minutes is $\frac{3}{25}$

Explanation:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}}=\frac{0.69}{k}$

$k=\frac{0.69}{110}=6.3\times 10^{-3}min^{-1}$

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

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

where,

k = rate constant  = $6.3\times 10^{-3}min^{-1}$

t = age of sample  = 20 min

a = let initial amount of the reactant = 100  

x=  amount that decay

a - x = amount left after decay process  =?

$20=\frac{2.303}{6.3\times 10^{-3}}\log\frac{100}{(a-x)}$

$(a-x)=88$

Thus fraction that decays = $\frac{(100-88)}{100}=\frac{3}{25}$

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