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 (t2âˆ’t1) 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(t1−t2)/T Given-* Activity at t=t1 is A1∗ Activity at t=t2 is A2 we know - activity A=A0e−λt=N0⋅λeλt⇒A1=A0⋅e−λt1 and A2=A0⋅e−λt2⇒A1=N0⋅λ⋅e−λt1A2=N0⋅λ⋅e−λt2 we have half life, t1/2=t2−t1A1−A2=N0λ[e−λt1−e−λt2] we have- λt/2=ln2⇒t1/2=ln2λ⇒A1−A2=N0(t2−t1)⋅ln2⋅[e−λt1−e−λt2]A1A2=N0λ⋅eλt1N0λ⋅e−λt2=eλt2−λt1⇒A2=A1eλ(t1t2)A2=A1e(t1−t2)/T Whre [T=1λ] mean life.

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