A) \[\frac{{{n}_{t}}}{t}\]
B) \[\ln \frac{{{n}_{t}}}{t}\]
C) \[\frac{d}{dt}(\ln \,nt)\]
D) \[t.{{n}_{t}}\]
Correct Answer: C
Solution :
We know that, Rate of disintegration \[=-\frac{dN}{dt}\propto N\] or \[\frac{-dN}{dt}=kN\](k = disintegration constant) Given, \[N={{n}_{t}}\]and \[t=t,\] \[\therefore \] \[\frac{-d{{n}_{t}}}{dt}=k{{n}_{t}}\] \[\Rightarrow \] \[\frac{-d{{n}_{t}}}{{{n}_{t}}}=kdt\] or \[\frac{-d\ln {{n}_{t}}}{dt}=k=\text{constant}\]
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