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 radius of a nucleus of a mass number A is directly proportional to [MH CET 1999; AMU (En.) 2001; UPSEAT 2004; DUMET 2010]

1. $A^3$ 

2. A 

3. $A^{2/3}$

4. $A^{1/3}$

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. $A_1{t}_1-A_2{t}_2$

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. $\lambda =\frac{{\log }_2 e}{T}$

If the nuclear force between two protons, two neutrons and between a proton and a neutron is denoted by $F_{pp},$ $F_{nn}$ $and$ $F_{pn}$ respectively, then:

1. $F_{pp}\approx F_{nn}\approx F_{pn}$

2. $F_{pp}\ne F_{nn}$ $and$ $F_{pn}=F_{nn}$

3. $F_{pp}=F_{nn}=F_{pn}$

4. $F_{pp}\ne F_{nn}\ne F_{pn}$

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