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 radium is 1622 years. How long will it take for seven-eighth of a given amount of radium to decay

1. 3244 years

2. 6488 years

3. 4866 years

4. 811 years

In a radioactive sample the fraction of initial number of radioactive nuclei, which remains undecayed after n mean lives is:

1. $\frac{1}{e^n}$ 

2.  $e^n$   

3. $1-\frac{1}{e^n}$ 

4. ${\left(\frac{1}{e-1}\right)}^n$

The activity of a radioactive sample is measured as 9750 counts/min at t = 0 and as 975 counts/min at t = 5 min. The decay constant is approximately:

1. 0.922/min           

2. 0.691/min         

3. 0.461/min           

4. 0.230/min

At time t = 0, N₁ nuclei of decay constant λ₁ and N₂ nuclei of decay constant λ₂ are mixed. The decay rate of the mixture is:

1. $-N_1{N}_2{e}^{-\left({\lambda }_1+{\lambda }_2\right)t}$ $$

2. $-\left(\frac{N_1}{N_2}\right)$ $e^{{}^{-\left({\lambda }_1+{\lambda }_2\right)t}}$ $$

3. $-\left(N_1{\lambda }_1{e}^{-{\lambda }_{1}t}\right)$ $+$ $N_2{\lambda }_2{e}^{-{\lambda }_{2}t}$ $$

4. $-N_1{\lambda }_1{N}_2{\lambda }_2{e}^{{}^{-\left({\lambda }_1+{\lambda }_2\right)t}}$

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

The radioactivity of a sample is $A_1$ at a time $t_1$ and $A_2$ at time $t_2$.  If the mean life of the specimen is T, the number of atoms that have disintegrated in the time interval of $t_2-t_1$ is:

1. $A_1-A_2$ 

2. $\frac{A_1-A_2}{T}$

3. $\left(A_1-A_2\right)T$

4. $A_1{t}_1-A_2{t}_2$

The relationship between disintegration constant $\left[\lambda \right]$ and half-life [T] will be:

1. $\lambda =\frac{{\log }_{10}<mspace\; width="1em"></mspace>2}{T}$ 

2. $\lambda =\frac{{\log }_e<mspace\; width="1em"></mspace>2}{T}$

3. $\lambda =\frac{T}{{\log }_e<mspace\; width="1em"></mspace>2}$   

4. $\lambda =\frac{{\log }_2<mspace\; width="1em"></mspace>e}{T}$

Alpha particles are 

1. 2 free protons

2. helium atoms

3. singly ionized helium atoms

4. doubly ionised helium atoms

A radioactive sample with a half-life of 1 month has the label: 'Activity = 2 microcurie on 1-8-1991'. What would be its activity two months earlier? 

1. 1.0 microcurie       

2. 0.5 microcurie           

3. 4 microcurie             

4. 8 microcurie