Half-lives of two radioactive elements A and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The number of nuclei remaining after time $t$ is given by $N = N_0 (1/2)^n$,where $n = t / T_{1/2}$ is the number of half-lives.For element $A$: $

Vedclass · Accepted Answer

$4: 5$

Vedclass · Answer

(C) The number of nuclei remaining after time $t$ is given by $N = N_0 (1/2)^n$,where $n = t / T_{1/2}$ is the number of half-lives.For element $A$: $T_{1/2, A} = 30 	ext{ min}$,$t = 120 	ext{ min}$.Number of half-lives $n_A = 120 / 30 = 4$.Remaining nuclei $N_A = N_0 (1/2)^4 = N_0 / 16$.Decayed nuclei $N'_A = N_0 - N_A = N_0 - N_0 / 16 = (15/16) N_0$.For element $B$: $T_{1/2, B} = 60 	ext{ min}$,$t = 120 	ext{ min}$.Number of half-lives $n_B = 120 / 60 = 2$.Remaining nuclei $N_B = N_0 (1/2)^2 = N_0 / 4$.Decayed nuclei $N'_B = N_0 - N_B = N_0 - N_0 / 4 = (3/4) N_0 = (12/16) N_0$.The ratio of decayed nuclei of $B$ to $A$ is $N'_B / N'_A = (12/16) N_0 / (15/16) N_0 = 12 / 15 = 4 / 5$.

Half-lives of two radioactive elements $A$ and $B$ are $30 \text{ minute}$ and $60 \text{ minute}$ respectively. Initially,the samples have an equal number of nuclei. After $120 \text{ minute}$,the ratio of the number of decayed nuclei of $B$ to that of $A$ will be:

Similar Questions

If the half-life of a radioactive sample is $10\, hours$,its mean life is .......... $hours$.

Two different radioactive elements with half-lives $T_1$ and $T_2$ have undecayed atoms $N_1$ and $N_2$ respectively present at a given instant. The ratio of their activities at that instant is

Two radioactive substances $A$ and $B$ have the same number of initial nuclei. If the half-lives of $A$ and $B$ are $1.5 \ days$ and $4.5 \ days$ respectively,then the ratio of the number of nuclei remaining in $A$ and $B$ after $9 \ days$ is

The relation between the mean life time $\tau$ and the half-life time $T_{1/2}$ of a radioactive substance is:

$A$ radioactive substance has a half-life of $60 \text{ minutes}$. During $3 \text{ hours}$,the amount of substance decayed would be: (in $\%$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module