The numbers of nuclei of a radioactive substance at time t = 0 are 1000 and 900 at time t = 2 sec. Then the number of nuclei at time t = 4 sec will be:

1. 800

2. 810 

3. 790 

4. 700

A nucleus ${}_Z{}^{A}X$ has mass represented by m(A, Z). If $m_p$ and $m_n$ denote the mass of proton and neutron respectively and BE is the binding energy (in MeV), then:
[2007]

1. BE = [m(A, Z) - Z$m_p$- (A - Z)$m_n$] $c^2$

2. BE = [Z$m_p$+ (A - Z)$m_n$- m(A,Z)] $c^2$

3. BE = [Z$m_p$+ A$m_n$- m(A, Z)] $c^2$

4. BE = m(A, Z) - Z$m_p$- (A, Z)$m_n$

Half-lives of two radioactive substances A and B respectively are 20 min and 40 min.  Initially, the samples of A and B have an equal number of nuclei. After 80 min the ratio of the remaining number of A and B nuclei is:

1. 1 : 16

2. 4 : 1

3. 1 : 4 

4. 1 : 1

Radioactive ${}_{27}{}^{60}Co$ is transformed into stable ${}_{28}{}^{60}Ni$ by emitting two $\gamma$-rays of energies

1. 1.33 MeV and 1.17 MeV in succession

2. 1.17 MeV and 1.33 MeV in succession

3. 1.37 MeV and 1.13 MeV in succession

4. 1.17 MeV and 1.13 MeV in succession

The volume occupied by an atom is greater than the volume of the nucleus by factor of about [2003]

1. ${10}^{10}$ 

2. ${10}^{15}$ 

3. ${10}^1$ 

4. ${10}^5$

A radioactive nucleus undergoes a series of decay according to the scheme 

$A\stackrel{\alpha }{\to }{A}_1\stackrel{\beta }{\to }{A}_2\stackrel{\alpha }{\to }{A}_3\stackrel{\gamma }{\to }{A}_4$

If the mass number and atomic number of A are 180 and 72 respectively, then what are these number for $A_4$?

1. 172 and 69 

2. 174 and 70

3. 176 and 69

4. 176 and 70

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