Question 190: Atoms & Nuclei

Question

If 'f' denotes the ratio of the number of nuclei decayed (N
d
) to the number of nuclei at t = 0 (N
0
) 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]

Accepted Answer

N = N
0
e
$$-$$$$\lambda$$t
N
d
= N
0
$$-$$ N
N
d
= N
0
(1 $$-$$ e
$$-$$$$\lambda$$t
)
$${{{N_d}} \over {{N_0}}} = f = 1 - {e^{ - \lambda t}}$$
$$ \Rightarrow $$ $${{df} \over {dt}} = \lambda {e^{ - \lambda t}}$$

Answer

$$-$$ $$\lambda$$ (1 $$-$$ e
$$-$$$$\lambda$$t
)

Answer

$$\lambda$$ (1 $$-$$ e
$$-$$$$\lambda$$t
)

Answer

$$\lambda$$e
$$-$$$$\lambda$$t

Answer

$$-$$ $$\lambda$$e
$$-$$$$\lambda$$t

Atoms & Nuclei

If 'f' denotes the ratio of the number of nuclei decayed (N d ) to the number of nuclei at t = 0 (N 0 ) 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]

Choose the correct answer: