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GATE 2021 BM – Question 34

Medical Imaging Systems · Nuclear Imaging · 1 mark · Numerical answer

A radionuclide has decay constant 3.22×10⁻⁵ s⁻¹ and activity 6 mCi at 10:30 AM. Find activity at 4:30 PM on the same day, in mCi to two decimals.

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Correct answer: 2.96 to 3.02

Explanation

The elapsed time is six hours=21600 seconds. Activity decays as A=A₀exp(−λt), giving A=6exp[−3.22×10⁻⁵×21600]≈2.99 mCi. The exponent is dimensionless because seconds match the decay-constant units. This lies in the official 2.96–3.02 interval.

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