Atomic weight of boron is 10.81 and it has two isotopes ${}_5{}^{10}B and {}_5{}^{11}B$. Then, the ratio of atoms of  ${}_5{}^{10}B and {}_5{}^{11}B$ in nature would be 

1. 19 : 81

2. 10 : 11 

3. 15 : 16 

4. 81 : 19

The half-life of radium is 1600 yr.  The fraction of a sample of radium that would remain

after 6400 yr [1991]

1. $\frac{1}{4}$   

2. $\frac{1}{2}$ 

3. $\frac{1}{8}$ 

4. $\frac{1}{16}$

The count rate of a Geiger Muller counter for the radiation of a radioactive material of half-life 30 min decreases to 5 $s^{-1}$ after 2 h. The initial count rate was [1995]

1. 20 $s^{-1}$ 

2. 25 $s^{-1}$ 

3. 80 $s^{-1}$ 

4. 625 $s^{-1}$

An element A decays into element C by a two step process

$A\to B+{}_{2}H{e}^4$
$B\to C+2e^{-}$

then  [1989]

1. A and C are isotopes

2. A and C are isobars

3. A and B are isotopes

4. A and B are isobars

The radius R of a nuclear matter varies with A as

1. $R \alpha A^{2/3}$

2. $R \alpha A^{1/3}$

3. $R \alpha A^0$ 

4. $R \alpha A$

Number of nuclei of a radioactive substance at time t = 0 are 2000 and 1800 at time t = 2s. Number of nuclei left after t = 6s is [MGIMS 2010]

1. 1442 

2. 1554 

3. 1652 

4. 1458

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. $R_1=R_2$

Which of the following are suitable for the fusion process ? [2002]

1. Light nuclei

2. Heavy nuclei

3. Elements lying in the middle of periodic table

4. Elements lying in the middle of binding energy curve

An archeologist analyses the wood in a prehistoric structure and finds that ${\mathrm{C}}^{14}$ (Half - life=5700 years) to ${\mathrm{C}}^{12}$ is only one - fourth of that found in the cells buried plants. The age of the wood is about

1. 5700 yr

2. 2850 yr

3. 11,400 yr

4. 22,800 yr

In the nuclear reaction: $X{(n,}_{}$ $\alpha )3L{i}^7$, the term X will be:

1. ${}_{5}B_{10}$ 

2. ${}_{5}B_9$

3. ${}_{5}B_{11}$

4. ${}_{2}H{e}^4$