The half-life of $^{238} _{92} U$ undergoing $\alpha$ -decay is $4.5 \times 10^{9}$ $years$. What is the activity of $1\; g$ sample of $^{238} _{92} U$?
The half-life of $^{238} _{92} U$ undergoing $\alpha$ -decay is $4.5 \times 10^{9}$ $years$. What is the activity of $1\; g$ sample of $^{238} _{92} U$?
$T_{1 / 2}=4.5 \times 10^{9}\, y$
$=4.5 \times 10^{9} y \times 3.16 \times 10^{7} \,s / y$
$=1.42 \times 10^{17}\, s$
One $k$ mol of any isotope contains Avogadro's number of atoms, and so lg of $^{238}_{92} U$ contains
$\frac{1}{238 \times 10^{-3}}\, kmol \times 6.025 \times 10^{26} \text { atoms } / kmol$
$=25.3 \times 10^{20}$ atoms.
The decay rate $R$ is $R=\lambda N$
$=\frac{0.693}{T_{1 / 2}} \,N=\frac{0.693 \times 25.3 \times 10^{20}}{1.42 \times 10^{17}} \,s ^{-1}$
$=1.23 \times 10^{4}\, s ^{-1}$
$=1.23 \times 10^{4}\; Bq$
Similar Questions
Match List $I$ (Wavelength range of electromagnetic spectrum) with List $II$ (Method of production of these waves) and select the correct option from the options given below the lists
List $I$
List $II$
$(1)$ $700\, nm$ to $1\,mm$
$(i)$ Vibration of atoms and molecules
$(2)$ $1\,nm$ to $400\, nm$
$(ii)$ Inner shell electrons in atoms moving from one energy level to a lower level
$(3)$ $ < 10^{-3}\,nm$
$(iii)$ Radioactive decay of the nucleus
$(4)$ $1\,mm$ to $0.1\,m$
$(iv)$ Magnetron valve
Match List $I$ (Wavelength range of electromagnetic spectrum) with List $II$ (Method of production of these waves) and select the correct option from the options given below the lists
| List $I$ | List $II$ |
| $(1)$ $700\, nm$ to $1\,mm$ | $(i)$ Vibration of atoms and molecules |
| $(2)$ $1\,nm$ to $400\, nm$ | $(ii)$ Inner shell electrons in atoms moving from one energy level to a lower level |
| $(3)$ $ < 10^{-3}\,nm$ | $(iii)$ Radioactive decay of the nucleus |
| $(4)$ $1\,mm$ to $0.1\,m$ | $(iv)$ Magnetron valve |
- [JEE MAIN 2014]
Half life of radioactive element depends upon
Half life of radioactive element depends upon
In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life .......... $\%$
In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life .......... $\%$
Two radioactive materials $A$ and $B$ have decay constants $25 \lambda$ and $16 \lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $B$ to that of $A$ will be "$e$" after a time $\frac{1}{a \lambda}$. The value of $a$ is $......$
Two radioactive materials $A$ and $B$ have decay constants $25 \lambda$ and $16 \lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $B$ to that of $A$ will be "$e$" after a time $\frac{1}{a \lambda}$. The value of $a$ is $......$
- [JEE MAIN 2022]
A radioactive material of half-life $T$ was produced in a nuclear reactor at different instants, the quantity produced second time was twice of that produced first time. If now their present activities are $A_1$ and $A_2$ respectively then their age difference equals :
A radioactive material of half-life $T$ was produced in a nuclear reactor at different instants, the quantity produced second time was twice of that produced first time. If now their present activities are $A_1$ and $A_2$ respectively then their age difference equals :