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Question

The activity of a sample of radioactive material is A1 at time t1 and A2 at time t2. Its half life is 1.no of atoms decade in time (t2t1) is proportional to?

A
A1A2
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B
A1A2t2t1=constant
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C
A2=A1e(t1t2)/T
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D
A2=A1e(t1/Tt2)
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Solution

The correct option is C A2=A1e(t1t2)/T
Given-* Activity at t=t1 is A1 Activity at t=t2 is A2 we know - activity A=A0eλt=N0λeλtA1=A0eλt1 and A2=A0eλt2A1=N0λeλt1A2=N0λeλt2

we have half life, t1/2=t2t1A1A2=N0λ[eλt1eλt2] we have- λt/2=ln2t1/2=ln2λA1A2=N0(t2t1)ln2[eλt1eλt2]


A1A2=N0λeλt1N0λeλt2=eλt2λt1A2=A1eλ(t1t2)A2=A1e(t1t2)/T Whre [T=1λ] mean life.

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