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

(B) Let $(T_H)_A$ and $(T_H)_B$ be the half-lives of substances $A$ and $B$ respectively.Given: $(T_H)_A = 2(T_H)_B$.Let $N_A$ and $N_B$ be the initia

Vedclass · Accepted Answer

$\frac{1}{8}$

Vedclass · Answer

(B) Let $(T_H)_A$ and $(T_H)_B$ be the half-lives of substances $A$ and $B$ respectively.Given: $(T_H)_A = 2(T_H)_B$.Let $N_A$ and $N_B$ be the initial number of nuclei.The number of nuclei remaining after time $t$ is given by $N(t) = N_0 \left(\frac{1}{2}\right)^{t/T_H}$.After time $t = 3(T_H)_A$,the number of nuclei of $A$ is $N_A(t) = N_A \left(\frac{1}{2}\right)^3 = \frac{N_A}{8}$.Since $(T_H)_A = 2(T_H)_B$,we have $t = 3(2(T_H)_B) = 6(T_H)_B$.The number of nuclei of $B$ after time $t$ is $N_B(t) = N_B \left(\frac{1}{2}\right)^6 = \frac{N_B}{64}$.Given that $N_A(t) = N_B(t)$,we have $\frac{N_A}{8} = \frac{N_B}{64}$.Therefore,$\frac{N_A}{N_B} = \frac{8}{64} = \frac{1}{8}$.

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 the ratio $\frac{N_A}{N_B}$ is

Similar Questions

The intensity of the electric field required to keep a water drop of radius $10^{-5} \, cm$ just suspended in air when charged with one electron is approximately:

The kind of tissue that forms the supportive structure in the pinna is also found in

Identify $A$ and $B$ in the following reactions:

In which of the following combinations is buffer action expected?
$A$. $NH_4OH + NH_4Cl$
$B$. $HCl + NaCl$
$C$. $NH_4OH + HCl$ in $2 : 1$ mole ratio
Select the correct answer using the code given below:

Example of a biodegradable polymer pair is

Vedclass Test Series

Exam Paper Generator

Online Exam Module