Question 191: Atoms & Nuclei

Question

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :
(where $$\lambda$$ is the decay constant)

Accepted Answer

$${{3{N_0}} \over 4} = {N_0}{e^{ - \lambda {t_1}}}$$
$${{{N_0}} \over 2} = {N_0}{e^{ - \lambda {t_2}}}$$
$$\ln (3/4) =  - \lambda {t_1}$$ ..... (i)
$$\ln (1/2) =  - \lambda {t_2}$$ ..... (i)
$$\ln (3/4) - \ln (1/2) = \lambda ({t_2} - {t_1})$$ ....(i)
$$\Delta t = {{\ln (3 /2)} \over \lambda }$$

Answer

$${1 \over 2}{{\ln 2} \over \lambda }$$

Answer

$${{\ln 2} \over \lambda }$$

Answer

$${{2\ln 2} \over \lambda }$$

Answer

$${{\ln {3 \over 2}} \over \lambda }$$

Atoms & Nuclei

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as : (where $\lambda$ is the decay constant)

Choose the correct answer: