Question

Derive relationship between half life and decay constant

Answer 1

Decay constant. Decay constant, proportionality between the size of a population of radioactive atoms and the rate at which the population decreases because of radioactive decay. ... The relationship between the half-life, T1/2, and the decay constant is given by T1/2 = 0.693/λ.

Answer 2

The relation between half life and decay constant is $t_{\frac{1}{2}}=\frac{0.693}{k}$

Explanation:

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

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

where,

k = decay constant  

t = age of sample

a = let initial amount of the reactant  

a - x = amount left after decay process  

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.

$t_{\frac{1}{2}}=\frac{2.303}{k}\log\frac{100}{50}$

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

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