If the activity of a radioactive sample drops to 1/32 of its initial value after 7.5 Hours, its half-life will be:

1. 3 Hours

2. 4.5 Hours

3. 7.5 Hours

4. 1.5 Hours

From a newly formed radioactive substance (Half-life 2 hours), the intensity of radiation is 64 times the permissible safe level. The minimum time after which work can be done safely from this source is:
1. 6 hours           
2. 12 hours
3. 24 hours         
4. 128 hours

The relation between λ and T_1/2 is:
(T_1/2 = half-life, λ → decay constant)

1. $T_{1/2}=\frac{\ln 2}{\lambda }$

2. $T_{1/2}$ $\ln 2=\lambda$

3. $T_{1/2}=\frac{1}{\lambda }$

4. $(\lambda +T_{1/2})=\frac{\ln }{2}$

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

If the half-life of a radionuclide is 77 days, then its decay constant is:
1.  0.003/day
2.  0.006/day
3.  0.009/day
4.  0.012/day

If the half-life of a radioactive substance is 10 hours, then its mean life is:

1.  14.4 h

2.  7.2 h

3.  20 h

4.  6.93 h

The half-life of a radioactive substance is 20 minutes. The time between 20% and 80% decay will be: 

1. 20 minutes

2. 40 minutes

3. 30 minutes

4. 25 minutes

In a radioactive substance at t = 0, the number of atoms is 8$\times {10}^4$, its half-life period is 3 yr. The number of atoms equal to $1\times {10}^4$ will remain after an interval of:

1. 9 yr

2. 8 yr 

3. 6 yr 

4. 24 yr

The half-life of a radioactive nucleus is 50 days. The time interval $({\mathrm{t}}_2-{\mathrm{t}}_1)$ between the time ${\mathrm{t}}_2$ when $\frac{2}{3}$ of it has decayed and the time ${\mathrm{t}}_1$ when $\frac{1}{3}$ of it had decayed is:

1. 30 days

2. 50 days

3. 60 days

4. 15 days

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. $R_1=R_2$