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(C) The rate of radioactive disintegration is given by the equation: $-\frac{dN}{dt} = \lambda N$. Here,$-\frac{dN}{dt}$ represents the number of atom

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Triple

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(C) The rate of radioactive disintegration is given by the equation: $-\frac{dN}{dt} = \lambda N$. Here,$-\frac{dN}{dt}$ represents the number of atoms disintegrating per unit time,$\lambda$ is the decay constant,and $N$ is the number of radioactive atoms present. Radioactive decay is a first-order nuclear process and is independent of external physical conditions like temperature,pressure,or concentration. Since the decay constant $\lambda$ remains unchanged with temperature,the rate of disintegration depends only on the number of atoms $N$. If the amount of substance $N$ is increased three times,the rate of disintegration $-\frac{dN}{dt}$ will also increase by a factor of $3$ (i.e.,it becomes triple).

If the amount of radioactive substance is increased three times and simultaneously the temperature is also increased three times,the number of atoms disintegrating per unit time would be

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