Law of Radioactivity

Q.

A freshly prepared radioactive source of half-life 2 hours emits radiations of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is

1. 12 hours
2. 24 hours
3. 128 hours
4. 6 hours

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.

If 12 g of sample is taken, and 6 g of a sample decays in 1 hr. The amount of sample showing decay in next hour is

1. 3 g
2. 1 g
3. 2 g
4. 6 g

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

Q. Amount of ${}_{53}{I}^{128}(t_{\frac{1}{2}}=25min)left$ after 75 minutes is

1. $\frac{1}{6}$
2. $\frac{1}{4}$
3. $\frac{1}{8}$
4. $\frac{1}{9}$

Q. In a radioactive sample the decrease in the number of active nuclei at any time is directly proportional to?

1. Number of radioactive nuclei present in the starting
2. Time elapsed from the start time
3. Number of radioactive nuclei present at that particular instant
4. A small time interval from that particular instant.

Q. Equal masses of two samples of charcoal A and B are burnt separately and the resulting carbon dioxide are collected in two vessels. The radioactivity of ${}^{14}C$ is measured for both the gas samples. The gas from the charcoal A gives 2100 counts per week and the gas from the charcoal B gives 1400 counts per week. Find the age difference between the two samples. Half-life of ${}^{14}C$ = 5730 y.

1. 2500 Years
2. 3352 Years
3. 4567 Years
4. 2392 Years

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

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

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

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

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

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. $e^2$

2. $e^{-1}$

3. $e^{-2}$

4. $e$