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

The half-life period of a radioactive element $x$ is the same as the mean life time of another radioactive element $y$. Initially,they have the same number of atoms. Then:

$A$ radioactive element $ThA$ $(_{84}Po^{216})$ can undergo $\alpha$ and $\beta$ types of disintegrations with half-lives $T_1$ and $T_2$ respectively. Then the effective half-life of $ThA$ is:

Two radioactive materials $M_1$ and $M_2$ have decay constants $9 \lambda$ and $\lambda$ respectively. Initially,they have the same number of nuclei. The ratio of the number of nuclei of $M_1$ to that of $M_2$ will be $\frac{1}{e}$ after a time interval of:

Define the average life of a radioactive substance.

The half-life of a radioactive substance is $25 \ min$. The time interval between $50 \%$ decay and $87.5 \%$ decay of the substance will be: (in $min$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module