(C) If $n_t$ is the number of radioactive atoms present at time $t$, radioactive decay follows the law:$n_t = n_0 e^{-\lambda t}$Taking the natural lo

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(C) If $n_t$ is the number of radioactive atoms present at time $t$, radioactive decay follows the law:$n_t = n_0 e^{-\lambda t}$Taking the natural logarithm on both sides:$\ln n_t = \ln n_0 - \lambda t$Differentiating with respect to time $t$:$\frac{d}{d t} (\ln n_t) = -\lambda$Since $\lambda$ (decay constant) is a constant, the expression $\frac{d \ln n_t}{d t}$ is constant.

Class 12 Chemistry Nuclear Chemistry Rate of decay and Half-life

Medium

If $n_t$ number of radioatoms are present at time $t$, the following expression will be a constant:

WBJEE 2009 All WBJEE

A
$n_t / t$
B
$\ln(n_t / t)$
C
$\frac{d \ln n_t}{d t}$
D
$t n_t$

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If $n_t$ number of radioatoms are present at time $t$, the following expression will be a constant:

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