The decay constant of a radioactive nuclide is 1.6 ×10^-3s^-1.At a given instant,the number of atoms of the radioactive nuclide is 1.85 ×10¹².The number of atoms of the nuclide that remain after a time interval of 30 minutes is closest to:

Question

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Explanation:The number of atoms remaining after a time interval t is given by:N(t) = N(0)e^(-λt)where N(0) is the initial number of atoms, λ is the decay constant, and t is the time interval.Substituting the given values into the equation, we get:N(30 min) = (1.85 × 10^12)e^(-1.6 × 10^-3 s^-1 × 30 min × 60 s/min)= (1.85 × 10^12)e^(-28.8)= 1.04 × 10^11Therefore, the number of atoms of the nuclide that remain after a time interval of 30 minutes is closest to 1.04 × 10^11.

The Decay Constant of a Radioactive Nuclide Is 1