What fraction of a radioactive material will get disintegrated in a period of two half-lives?

1. whole

2. half

3. one-fourth

4. three-fourth

If the nucleus ${}_{13}{}^{27}Al$ has a nuclear radius of about 3.6 fm, then ${}_{52}{}^{125}Te$ would have its radius approximately as [2007]

1. 6.0 fm 

2. 9.6 fm

3. 12.0 fm 

4. 4.8 fm

After two hours, one-sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half life of the isotope is [Bihar MEE 1995; Manipal MEE 1995; MP PMT 1997; AFMC 2000, 05; DPMT 2002]

1. 15 minutes 

2. 30 minutes

3. 45 minutes

4. 1 hour

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 $s^{-1}$

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. $R_1=R_2$