Question

- A sample of 32P initially shows -activity
of one Curie. After 303 days the activity
falls to 1.5 x 104 dps. What is the half life
of 32P ?
(Ans.14.27 d)​

Answer 1

The half life  of P-32 is 6.3 days

Explanation:

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  

t = age of sample

a = let initial amount of the reactant  = 1 Curie = $3.7\times 10^{10}dps$

a - x = amount left after decay process  = $1.5\times 10^{4}dps$

$303=\frac{2.303}{k}\log\frac{3.7\times 10^{10}}{1.5\times 10^{4}}$

$k=0.113days^{-1}$

For completion of half life:  

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

$t_{\frac{1}{2}}=\frac{0.693}{0.11}$

$t_{\frac{1}{2}}=6.3days$

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