A radioactive sample of U^{238} decays to Pb | vedclass

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

Question

(B) The number of half-lives $n$ is given by $n = \frac{t}{T_{1/2}} = \frac{1.5 	imes 10^9}{4.5 	imes 10^9} = \frac{1}{3}$.The remaining number of $

Vedclass · Accepted Answer

$0.26$

Vedclass · Answer

(B) The number of half-lives $n$ is given by $n = \frac{t}{T_{1/2}} = \frac{1.5 	imes 10^9}{4.5 	imes 10^9} = \frac{1}{3}$.The remaining number of $U^{238}$ nuclei $N_U$ is given by $N_U = N_0 \left( \frac{1}{2} ight)^n = N_0 \left( \frac{1}{2} ight)^{1/3}$.Given $2^{1/3} = 1.26$,we have $\left( \frac{1}{2} ight)^{1/3} = \frac{1}{1.26} \approx 0.7937$.Thus,$N_U = N_0 	imes 0.7937$.The number of $Pb$ nuclei formed is $N_{Pb} = N_0 - N_U = N_0(1 - 0.7937) = N_0(0.2063)$.Alternatively,using the ratio: $\frac{N_U}{N_0} = \frac{1}{1.26}$.Since $N_0 = N_U + N_{Pb}$,we have $\frac{N_U}{N_U + N_{Pb}} = \frac{1}{1.26}$.$1.26 N_U = N_U + N_{Pb} \implies N_{Pb} = 0.26 N_U$.Therefore,the ratio $\frac{N_{Pb}}{N_U} = 0.26$.

$A$ radioactive sample of $U^{238}$ decays to $Pb$ through a process for which the half-life is $4.5 \times 10^9$ years. Find the ratio of the number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 \times 10^9$ years (given $2^{1/3} = 1.26$).

Similar Questions

For a certain radioactive process,the graph between $\ln R$ and $t \, (\text{sec})$ is obtained as shown in the figure. Then the value of the half-life for the unknown radioactive material is approximately $.... \, \text{sec}$.

$A$ radioactive substance decays by $10\%$ in $5$ days. What percentage of the original substance will remain after $20$ days (in $\%$)?

The decay constants of two radioactive elements are $15x$ and $3x$ respectively. Initially,they have the same number of nuclei. After a time of $\frac{1}{6x}$,the ratio of the number of their nuclei will be ........

The half-lives of $X$ and $Y$ are $3 \ min$ and $27 \ min$ respectively. If they have the same activity at a certain instant,find the ratio of the number of excited nuclei of $X$ and $Y$ at that instant.

The half-life of a radioactive element is $10 \, days$. The time required for the mass of the sample to reduce to $\frac{1}{10}$ of its initial mass is approximately ........ days.

Vedclass Test Series

Exam Paper Generator

Online Exam Module