The decay constant of a radio isotope is $\mathrm{\lambda }.$ If ${\mathrm{A}}_1$ and ${\mathrm{A}}_2$ are its activities at times ${\mathrm{t}}_1$ and ${\mathrm{t}}_2$ respectively, the number of nuclei which have decayed during the time $({\mathrm{t}}_1-{\mathrm{t}}_2)$

1. ${\mathrm{A}}_1{\mathrm{t}}_1-{\mathrm{A}}_2{\mathrm{t}}_2$                                       

2. ${\mathrm{A}}_1-{\mathrm{A}}_2$

3. $\frac{({\mathrm{A}}_1-{\mathrm{A}}_2)}{\mathrm{\lambda }}$                                       

4. $\mathrm{\lambda }({\mathrm{A}}_1-{\mathrm{A}}_2)$ 

The binding energy per nucleon in deuterium and helium nuclei are $1.1 \mathrm{MeV}$ and $7.0 \mathrm{MeV},$ respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is 

1. $23.6 \mathrm{MeV}$                                         

2. $2.2 \mathrm{MeV}$

3. $28.0 \mathrm{MeV}$                                         

4. $30.2 \mathrm{MeV}$

Two radioactive material $X_1$ and $X_2$ have decay constants $5\lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei of $X_1$to that of $X_2 will be \frac{1}{e}$after a time 

1. $\lambda$                                     

2. $\frac{1}{2}\lambda$

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

4. $\frac{e}{\lambda }$

One nanogram of matter converted into energy will give- 

1. 90 J                     

2. $9\times {10}^3 \mathrm{J}$ 

3. $9\times {10}^{10} \mathrm{J}$            

4. $9\times {10}^4 \mathrm{J}$

Fast neutrons can easily be slowed down by 

1. The use of lead shielding

2. Passing them through heavy water

3. Elastic collisions with heavy nuclei

4. Applying a strong electric field

The number of neutrons released when ${}_{92}\mathrm{U}_{235}$ undergoes fission by absorbing ${}_0{}^1\mathrm{n}$ and $\left({}_{56}{}^{144}\mathrm{Ba}+{}_{36}{}^{89}\mathrm{Kr}\right)$are formed, is 

1. 0           

2. 1

3. 2           

4. 3

The binding energy of nucleus is a measure of its

1. Charge             

2. Mass

3. Momentum       

4. Stability

Heavy water is 

1. Water at 4$°\mathrm{C}$

2. Compound of deuterium and oxygen

3. Compound of heavy oxygen and heavy hydrogen

4. Water in which soap does not lather

The decay constant of radium is $4.28\times {10}^{-4}$ per year. Its half life will be 

1. 2000 years       

2. 1240 years

3. 63 years           

4. 1620 years