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Question: The activity of a sample of radioactive material is A<sub>1</sub> at time t<sub>1</sub> and A<sub>2<...

The activity of a sample of radioactive material is A1 at time t1 and A2 at time t2(t2> t1). Its mean life is T then which of the following is correct?

A

A1t1 = A2t2

B

A1+A2t2–t1\frac{A_{1} + A_{2}}{t_{2}–t_{1}} = constant

C

A2=A1e(t1–t2)/TA_{2} = A_{1}e^{(t_{1}–t_{2})/T}

D

A2=A1e(t1/Tt2)A_{2} = A_{1}e^{(t_{1}/Tt_{2})}

Answer

A2=A1e(t1–t2)/TA_{2} = A_{1}e^{(t_{1}–t_{2})/T}

Explanation

Solution

A1 =

A 2 = A0e−t2/T\mathrm { A } _ { 0 } \mathrm { e } ^ { - \mathrm { t } _ { 2 } / \mathrm { T } }

= e(t1−t2)/Te ^ { \left( t _ { 1 } - t _ { 2 } \right) / T }

A 2 =