In the semi-log plot of (ordinate) versus time (abscissa) for a radioactive sample

PHYSICS · Subjective · CBSE · Physics · Nuclei · Nuclei

Problem

In the semi-log plot of log⁡10A\log_{10}A (ordinate) versus time (abscissa) for a radioactive sample, the straight line falls from 3.60 to 2.40 in 50 h. (i) Calculate the numerical value of the slope of the line. (ii) Hence determine the decay constant λ\lambda (in h−1^{-1}) and the half-life of the isotope. (iii) If the sample initially contains 1.5 mg of the isotope (pure, atomic mass = 60 u), estimate the mass that will remain after 200 h.

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