What fraction of a radioactive material will get disintegrated in a period of two half-lives?

1. whole

2. half

3. one-fourth

4. three-fourth

In a radioactive material, the activity at time $t_1$ is $R_1$ and at a later time, $t_2$ is $R_2$. If the decay constant of the material is $\lambda$, then:

1. $R_1=R_2{e}^{-\lambda \left(t_1-t_2\right)}$   

2. $R_1=R_2{e}^{\lambda \left(t_1-t_2\right)}$

3. $R_1=R_2\left(\frac{t_2}{t_1}\right)$ 

4. $R_1=R_2$

A and B are two radioactive substances whose half-lives are 1 and 2 years respectively. Initially 10 g of A and 1 g of B is taken. The time (approximate) after which they will have the same quantity remaining is:

1. 6.62 yr

2. 5 yr   

3. 3.2 yr 

4. 7 yr

Two radioactive substances A and B have decay constant 5λ and λ respectively. At t = 0 they have the same number of nuclei. The ratio of the number of nuclei of A to those of B will be (1/e)² after a time interval of:

1. $\frac{1}{4\mathrm{\lambda }}$ $$ $$

2. $4\mathrm{\lambda }$ $$ $$

3. $2\mathrm{\lambda }$ $$

4. $$ $\frac{1}{2\mathrm{\lambda }}$

The activity of the radioactive element decreases to one-third of the original activity ${\mathrm{A}}_0$ in a period of 7 years. After a further lapse of 7 years, its activity will be:

1.  ${\mathrm{A}}_0$ $$ $$

2.  $\frac{2}{3}{\mathrm{A}}_0$ $$ $$

3.  $\frac{{\mathrm{A}}_0}{6}$ $$ $$

4.  $\frac{{\mathrm{A}}_0}{9}$

A radioactive nucleus X decays to a stable nucleus 'y'. The graph of the rate of formation of 'y' against time 't' will be:

1.		2.
3.		4.

Half-lives of two radioactive substances A and B respectively are 20 min and 40 min.  Initially, the samples of A and B have an equal number of nuclei. After 80 min the ratio of the remaining number of A and B nuclei is:

1. 1 : 16

2. 4 : 1

3. 1 : 4 

4. 1 : 1

The counting rate observed from a radioactive source at t = 0 second was 1600 counts per second and at t = 8 seconds it was 100 counts per second. The counting rate observed, as counts per second, at t = 6 seconds will be:

1. 400

2. 300

3. 200

4. 150

The rate of disintegration of a fixed quantity of a radioactive substance can be increased by:

1. increasing the temperature.

2. increasing the pressure.

3. chemical reaction.

4. it is not possible.

The half-life period of a radioactive substance is 6 h.  If after 24 h, activity is 0.01 $\mu$Ci, what was the initial activity? 

1. 0.04 $\mu$Ci 

2. 0.08 $\mu$Ci

3. 0.24 $\mu$Ci 

4. 0.16 $\mu$Ci