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Question

(d) Activity $A = \lambda \;{N_0}{e^{ - \lambda t}}$

==>${\log _e}A = {\log _e}\lambda \,{N_0} + {\log _e}{e^{ - \lambda t}}$

==> ${\log _

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$D$

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(d) Activity $A = \lambda \;{N_0}{e^{ - \lambda t}}$

==>${\log _e}A = {\log _e}\lambda \,{N_0} + {\log _e}{e^{ - \lambda t}}$

==> ${\log _e}A = {\log _e}C - \lambda t$       (Take $\lambda  N_0 = C$)

==> ${\log _e}A = - \lambda t + {\log _e}C$

This is the equation of a straight line having negative slope ($= -\lambda$) and positive intercept on ${\log _e}A$ axis.

The graph which represents the correct variation of logarithm of activity $(log\, A)$ versus time, in figure is

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