A radioactive nucleus A has a single decay mo | vedclass

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

Question

(A) For a radioactive nucleus with multiple decay modes,the total decay constant $\lambda_B$ is the sum of the individual decay constants: $\lambda_B

Vedclass · Accepted Answer

$3 / 7$

Vedclass · Answer

(A) For a radioactive nucleus with multiple decay modes,the total decay constant $\lambda_B$ is the sum of the individual decay constants: $\lambda_B = \lambda_1 + \lambda_2$.Since the decay constant $\lambda$ is related to the half-life $	au$ by $\lambda = \ln(2) / 	au$,we can write the relationship as $1 / 	au_B = 1 / 	au_1 + 1 / 	au_2$.Given that if decay mode $2$ were absent,the half-life is $	au_1 = 	au_A / 2$.Given that if decay mode $1$ were absent,the half-life is $	au_2 = 3 	au_A$.Substituting these into the formula for the actual half-life $	au_B$:$1 / 	au_B = 1 / (	au_A / 2) + 1 / (3 	au_A)$$1 / 	au_B = 2 / 	au_A + 1 / (3 	au_A)$$1 / 	au_B = (6 + 1) / (3 	au_A) = 7 / (3 	au_A)$Therefore,$	au_B = (3 / 7) 	au_A$,which implies $	au_B / 	au_A = 3 / 7$.

Similar Questions

The activity of a radioactive sample is measured as $9750$ counts per minute at $t = 0$ and as $975$ counts per minute at $t = 5$ minutes. The decay constant is approximately ............ per minute.

Two radioactive materials $X_1$ and $X_2$ have decay constants $5\lambda$ and $\lambda$ respectively. Initially,they have the same number of nuclei. The ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $\frac{1}{e}$ after a time:

At a certain moment,the amounts of two radioactive substances are in the ratio $2:1$. Their half-lives are $12 \text{ hours}$ and $16 \text{ hours}$ respectively. What will be the ratio of their remaining amounts after $2 \text{ days}$?

The half-life of a radioactive substance against $\alpha$-decay is $1.2 \times 10^7 \, s$. What is the decay rate for $4.0 \times 10^{15}$ atoms of the substance?

The mean life of a radioactive material for alpha decay and beta decay are,respectively,$1620$ years and $520$ years. What is the half life of the sample (in years)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module