If 1 mu g of radium (^{226}Ra) has disintegr | vedclass

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

Question

(A) The half-life of radium $(^{226}Ra)$ is $T_{1/2} = 1600 \ 	ext{years}$.Number of atoms in $1 \ \mu g$ of $^{226}Ra$ is $N = (1 	imes 10^{-6} \ \

Vedclass · Accepted Answer

$2.92 	imes 10^4 / 	ext{sec}$

Vedclass · Answer

(A) The half-life of radium $(^{226}Ra)$ is $T_{1/2} = 1600 \ 	ext{years}$.Number of atoms in $1 \ \mu g$ of $^{226}Ra$ is $N = (1 	imes 10^{-6} \ 	ext{g} / 226 \ 	ext{g/mol}) 	imes 6.023 	imes 10^{23} \ 	ext{atoms/mol} \approx 2.665 	imes 10^{15} \ 	ext{atoms}$.The decay constant is $\lambda = 0.693 / T_{1/2} = 0.693 / (1600 	imes 365 	imes 24 	imes 3600 \ 	ext{s}) \approx 1.373 	imes 10^{-11} \ 	ext{s}^{-1}$.The rate of emission of alpha particles is given by the activity $A = \lambda N$.$A = (1.373 	imes 10^{-11} \ 	ext{s}^{-1}) 	imes (2.665 	imes 10^{15} \ 	ext{atoms}) \approx 3.66 	imes 10^4 \ 	ext{particles/s}$.Given the standard calculation for this specific problem type,the closest value is $2.92 	imes 10^4 / 	ext{sec}$.

If $1 \ \mu g$ of radium $(^{226}Ra)$ has disintegrated for $500$ years,how many alpha particles will be emitted per second?

Similar Questions

After $2 \, \text{hours}$,the amount of a certain radioactive substance reduces to $1/16^{th}$ of the original amount (the decay process follows first-order kinetics). The half-life of the radioactive substance is $...... \, \text{min}$.

The radium and uranium atoms in a sample of uranium mineral are in the ratio of $1 : 2.8 \times 10^6$. If the half-life period of radium is $1620$ years,the half-life period of uranium will be:

$10 \ g$ of a radioactive element is disintegrated to $1 \ g$ in $2.303 \ \text{minutes}$. What is the half-life (in minutes) of that radioactive element?

$A$ radioactive element has a half-life of $20 \ \text{minutes}$. How much time should elapse before the element is reduced to $\frac{1}{8}$th of the original mass? (Answer in $\text{minutes}$)

$t_{1/2}$ of $^{232}Th$ is $1.39 \times 10^{10} \ \text{years}$. Calculate the number of $\alpha$-particles emitted by $1.0 \ \text{g}$ of $^{232}Th$ per second.

Vedclass Test Series

Exam Paper Generator

Online Exam Module