Half-life of a radioactive substance A is two | vedclass

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

Question

(D) Let the half-life of substance $B$ be $T_B = T$. Then the half-life of substance $A$ is $T_A = 2T$.After time $t$, the number of nuclei remaining

Vedclass · Accepted Answer

$\frac{1}{8}$

Vedclass · Answer

(D) Let the half-life of substance $B$ be $T_B = T$. Then the half-life of substance $A$ is $T_A = 2T$.After time $t$, the number of nuclei remaining is given by $N(t) = N_0 \left(\frac{1}{2}\right)^{t/T_{1/2}}$.The time elapsed is $t = 3 T_A = 3(2T) = 6T$.At this time, the number of nuclei of $A$ is $N_A(t) = N_A \left(\frac{1}{2}\right)^3$.At this time, the number of nuclei of $B$ is $N_B(t) = N_B \left(\frac{1}{2}\right)^{t/T_B} = N_B \left(\frac{1}{2}\right)^{6T/T} = N_B \left(\frac{1}{2}\right)^6$.Given that $N_A(t) = N_B(t)$, we have $N_A \left(\frac{1}{2}\right)^3 = N_B \left(\frac{1}{2}\right)^6$.Therefore, $\frac{N_A}{N_B} = \frac{(1/2)^6}{(1/2)^3} = \left(\frac{1}{2}\right)^{6-3} = \left(\frac{1}{2}\right)^3 = \frac{1}{8}$.

Half-life of a radioactive substance $A$ is two times the half-life of another radioactive substance $B$. Initially, the number of nuclei of $A$ and $B$ are $N_A$ and $N_B$ respectively. After three half-lives of $A$, the number of nuclei of both are equal. Then $\frac{N_A}{N_B}$ is

Similar Questions

Define the average life of a radioactive sample and obtain its relation to decay constant and half-life.

The half-life of a radioactive nucleus is $50$ days. The time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it had decayed and the time $t_1$ when $\frac{1}{3}$ of it had decayed is (in days):

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

The half-life of a radioactive element is $20 \, minutes$. What is the time interval (in $minutes$) between $33\%$ decay and $67\%$ decay?

$A$ radioactive element $A$ converts into another stable element $B$. The half-life of $A$ is $1.5 \ hrs$. After time $t$,the ratio of the number of atoms of $A$ to $B$ is found to be $1:8$. Then $t$ in hours is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module