Physics

Problem

Radioactive decay follows

N=N_0e^{-\lambda t}

. (i) Starting from this expression, obtain an equation of the form

\ln N = m t + c

and identify the physical significance of the slope

m

and intercept

c

. (ii) In an experiment on isotope X the straight-line extension of the

\ln N

versus

t

graph meets the time axis (where

\ln N = 0

) at

t=-3.0\,\text{min}

. The measured slope of the graph is

-0.025\,\text{min}^{-1}

. Calculate the initial number of nuclei present in the sample. (iii) Comment qualitatively on how random scatter in the data points would influence the accuracy of the half-life obtained from such a graph. a. (i) Derivation of straight-line form and identification of slope and intercept b. (ii) Calculation of initial number of nuclei using intercept and slope c. (iii) Qualitative comment on effect of experimental scatter

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