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

Binding energy per nucleon plot against the mass number for stable nuclei is shown in the figure. Which curve is correct ?

1. A
2. B
3. C
4. D

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. $30.2 \mathrm{MeV}$