Law of Radioactivity

Q. An old sample of wood from an archaeological excavation was found to have a radioactivity of about 140.8 counts per minute due to ${}^{14}C(t_{1/2}=5730$ years) as against 281.6 counts per minute for that of a freshly cut piece of wood. What is the age of the old sample of wood (in millennia, 1 millennium= 1000 years)?

Q.

If t is the time required for a radioactive substance to reduce to one third of its initial amount, what fraction would be left over after0.5 t

1. $\frac{1}{2}$

2. $\frac{1}{\sqrt{2}}$

3. $\frac{1}{\sqrt{3}}$

4. $\sqrt{\frac{2}{3}}$

Q. A certain nuclide has a half-life period of 30 minutes. If a sample containing 600 atoms is allowed to decay for 90 minutes, how many atoms will remain

1. 200 atoms

2. 450 atoms

3. 75 atoms
4. 500 atoms

Q. A certain nuclide has a half-life period of 30 minutes. If a sample containing 600 atoms is allowed to decay for 90 minutes, how many atoms will remain

1. 75 atoms
2. 200 atoms
3. 500 atoms

4. 450 atoms

Q.

Two radioactive elements X and Y have decay constants$\lambda$ and $10\lambda$ respectively. If decay begins with the same number of atoms of them, the ratio of atoms of X to those of Y after time $\frac{1}{9\lambda }$ will be

1. $e$

2. $e^{-1}$

3. $e^2$

4. $e^{-2}$

Q.

Two radioactive elements X and Y have decay constants$\lambda$ and $10\lambda$ respectively. If decay begins with the same number of atoms of them, the ratio of atoms of X to those of Y after time $\frac{1}{9\lambda }$ will be

1. $e$

2. $e^{-1}$

3. $e^2$

4. $e^{-2}$

Q.

If t is the time required for a radioactive substance to reduce to one third of its initial amount, what fraction would be left over after0.5 t

1. $\frac{1}{2}$

2. $\frac{1}{\sqrt{2}}$

3. $\sqrt{\frac{2}{3}}$

4. $\frac{1}{\sqrt{3}}$

Q. A radioactive sample had an initial activity of 56 dpm. After 69.3 minutes, it was found to have an activity of 28 dpm. Find the number of atoms in a sample that has an activity of 100 dpm.

1. 693
2. 100
3. 1000
4. 10, 000

Q. A radioactive isotope has a half-life of 10 days. If today 125 mg is left over, what was its original weight 40 days earlier

1. 2 g
2. 600 mg
3. 1 g
4. 1.5 g

Q. During the nuclear explosion, one of the products is ${}^{90}\text{Sr}$ with half life of 6.93 years. If 1 $\mu g$ of ${}^{90}\text{Sr}$ was absorbed in the bones of a newly born baby in place of $Ca$, how much time, in years, is required to reduce it by 90% if it is not lost metabolically?

Q. You have prepared a nice sample of $N_0$ radioactive nuclei of decay constant $\lambda$, and want to show it off to your friends. When they arrive units of time later, you open the lid and find there are only ___nuclei left intact.

1. $N_0{e}^{\lambda t}$
2. $N_0{e}^{-\lambda t}$
3. $N_0$
4. $N_0\lambda t$

Q. The activity of a radioactive nuclide $\left(X^{100}\right)$ is $6.023$ curie at a certain time $‘t^{\prime }$. If its disintegration constant is $3.7\times {10}^4{s}^{-1}$ the mass of $X$ after t sec is:

1. $6.022\times {10}^{6}g$
2. ${10}^{-13}g$
3. ${10}^{-15}g$
4. ${10}^{-17}g$