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If ' f ' denotes the ratio of the number of nuclei decayed \(\left({N}_{d}\right)\) to the number of nuclei at \(t=0\lef…

Q1

If ' f ' denotes the ratio of the number of nuclei decayed \(\left({N}_{d}\right)\) to the number of nuclei at \(t=0\left({\mathrm{N}}_{0}\right)\) then for a collection of radioactive nuclei, the rate of change of ' f ' with respect to time is given as: [ \(\lambda\) is the radioactive decay constant]

[JEE Main 2021, 27 Jul (Shift 1)]

a

\(\lambda {e}^{-\lambda t}\)

b

\(\lambda \left(1-{e}^{-\lambda i}\right)\)

c

\(-\lambda \left(1-{e}^{-\lambda \lambda }\right)\)

d

\(-\lambda {e}^{-\lambda t}\)

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