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Disintegration rate of a sample is 1010 per hour at 20 hrs from the start. It reduces to 6.3 × 109 per hour after 30 hours. Calculate its half life and the initial number of radioactive atoms in the sample.

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Data : A (t1 ) = 1010 per hour, where t1 = 20 h,

A (t2) = 6.3 × 109 per hour, where t2 = 30 h

A(t) = A0 \(e^{-\lambda t}\) 

∴ A(t1) = A0 \(e^{-\lambda t_1}\) and A(t2) = A0\(e^{-\lambda t_2}\)

∴ 1.587 e10λ ∴ 10λ =2.3031og10 (1.587) 

∴ λ = (0.2303)(0.2007) = 0.04622 per hour

The half life of the material, T1/2

This is the initial number of radioactive atoms in the sample.

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