Question

What is half life time of radioactive substance establish the relation between half time time and decay constant

Answer 1

The time required for half of the original population of radioactive atoms to decay is called the half-life. The relationship between the half-life, T1/2, and the decay constant is given by T1/2 = 0.693/λ.

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Answer 2

What is half life time of radioactive substance ? establish the relation between half time time and decay constant.

solution : half life of a radioactive substance is the time period in which the radioactive substance becomes half of its initial value.

for instance, if N is the initial amount of a radioactive substance.

and after time t, it becomes N/2 then t is known as half life of given radioactive substance.

we know, radioactive decay is a first order reaction which is given by,

$N(t)=N_0e^{-\lambda t}$

To derive half life,

N(t) = $\frac{N_0}{2}$

$t=T_{1/2}$

so, $\frac{N_0}{2}=N_0e^{-\lambda T_{1/2}}$

⇒$\frac{1}{2}=e^{-\lambda T_{1/2}}$

⇒$ln2=\lambda T_{1/2}$

⇒$T_{1/2}=\frac{ln2}{\lambda}$

Therefore the relation between half life and decay constant is $T_{1/2}=\frac{ln2}{\lambda}$