Three fourth of the active nuclei decay in a radioactive sample in 3/4 s. The half-life of the sample is

1. $\frac{1}{2} s$ 

2. 1 s   

3. $\frac{3}{8} s$ 

4. $\frac{3}{4} s$

Which of the following statements is true for nuclear forces? [1990]

1. They obey the inverse square law of distance.

2. They obey the inverse third power law of distance.

3. They are short range forces.

4. They are equal in strength to electromagnetic forces.

The ratio of the radii of the nuclei ${}_{13}A{l}^{27}$ and ${}_{52}T{e}^{125}$ is approximately [1990]

1. 6 : 10

2. 13 : 52 

3. 40 : 177

4. 14 : 73

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

1. $\lambda =\frac{{\log }_{10} 2}{T}$ 

2. $\lambda =\frac{{\log }_e 2}{T}$

3. $\lambda =\frac{T}{{\log }_e 2}$   

4. $\lambda =\frac{{\log }_2 e}{T}$

A radioactive element has half-life period 800 yr. After 6400 yr, what fraction will remain? [1989]

1. $\frac{1}{2}$

2. $\frac{1}{16}$ 

3. $\frac{1}{8}$ 

4.$\frac{1}{256}$

If radius of the ${}_{12}{}^{27}Al$ nucleus is taken to be $R_{Al}$, then the radius of ${}_{53}{}^{125}Te$ nucleus is nearly 

1. $\frac{5}{3}{R}_{Al}$ 

2. $\frac{3}{5}{R}_{Al}$ 

3. ${\left(\frac{13}{53}\right)}^{1/3}{R}_{Al}$ 

4. ${\left(\frac{53}{13}\right)}^{1/3}{R}_{Al}$

In a given reaction,

${}_{Z}X_A\to {}_{Z+1}Y_A\to {}_{Z-1}K_{A-4}\to {}_{Z-1}K_{A-4}$

Radioactive radiations are emitted in the sequence of  

1.  $\alpha , \beta , \gamma$ 

2. $\gamma , \alpha , \beta$ 

3. $\beta , \alpha , \gamma$ 

4. $\gamma , \beta , \alpha$

A sample of radioactive element has a mass of 10 g at an instant t = 0. The approximate mass of this element in the sample after two mean lives is [2003]

1. 3.70 g

2. 6.30 g

3. 1.35 g

4. 2.50 g

The mass density of a nucleus varies with mass number A as [1992]

1. $A^2$

2. A 

3. Constant 

4. $\frac{1}{A}$