Question

Explain, in words, the meaning of half-life. Furthermore, explain why we use half-life, instead of just the time it takes for a given radioisotope to decay to zero. [2 marks]

Context: Nuclear physics

Answer 1

Concept of half-life for radioactive material is introduced by Rutherford in 1904. The concept is very simple, Half-life is the time in which the number of radioactive nuclides reduce to half by disintegration.eg. suppose we have 10000 nuclides of any element right now and their half life is 24 hours then after 24 hours we left with 500 nuclides and after 48 hours we left wih 250 nuclides and so on.(i.e. after each half life, no of radioactive nuclides reduce to half. Half-life of a radioactive material is its intrinsic characteristic property that cannot be altered by physical or chemical process.

Derivation :  suppose we have N₀ number of radioactive nuclei present originally and if half-life of a radioactive substance is T, then at t=T , N=N₀ / 2

We know  N=N₀ exp(-t) (where is decay constant its unit is (second)^-1 )

N₀/2=N₀ exp(-T)

1/2=exp(-T)

T=0.693 /

Thus, half-life of a radioactive material depends upon the disintegration constant .

Your,next question (Why Half-life study ?)

Radioactive decay is a random phenomenon.Our sample contain huge number of nuclides(of order of avogrado number) we cannot say which nuclides will decay when.Thus some nuclides may decay at once, while others may have extremely long lives. It may take very long time(may say infinite time) for given radioisotope to decay to zero.So, half-life is easy to study we can sure about half-life of a sample but for full-life time no one can sure.

Besides this It is also a mathematical tool for us.By, studying half life of a sample we can find its decay constant ( =0.693/(half-life time) ) and now we use equation N = N₀ exp(-t) to find the number of nuclei left undecayed at any instant t.