Question

Tritium has a half life of 12.5 years against beta decay what fraction of sample of pure tritium will remain undecayed after 25 yrs

Answer 1

undecayed fraction is 3/4

Answer 2

$\frac{3}{4}$ fraction of sample of pure tritium will remain undecayed after 25 yrs

Explanation:

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

$t_{\frac{1}{2}}=\frac{0.693}{k}$

$k=\frac{0.693}{12.5}=0.055years^{-1}$

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  = $0.055years^{-1}$

t = time of decomposition = 25 years

a = let initial amount of the reactant  

a - x = amount left after decay process  

$25=\frac{2.303}{0.055}\log\frac{100}{(a-x)}$

$0.60=\log\frac{100}{(a-x)}$

$\frac{100}{(a-x)}=antilog(0.60)$

$\frac{100}{3.98}=(a-x)$

$(a-x)=25$

Fraction of sample of pure tritium decayed=$\frac{25}{100}=\frac{1}{4}$

Fraction of sample of pure tritium undecayed=$1-\frac{1}{4}=\frac{3}{4}$

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