In a radioactive substance at t = 0, the number of atoms is 8$\times {10}^4$, its half-life period is 3 yr. The number of atoms equal to $1\times {10}^4$ will remain after an interval of:

1. 9 yr

2. 8 yr 

3. 6 yr 

4. 24 yr

What is the respective number of $\alpha$ and $\beta$-particles emitted in the following radioactive decay?

$X_{90}^{{}_{200}}\to {}_{}Y_{80}^{168}$ 

1. 6 and 8

3. 6 and 6

3. 8 and 8

4. 8 and 6   

The half-life of radium is 1622 years. How long will it take for seven-eighth of a given amount of radium to decay

1. 3244 years

2. 6488 years

3. 4866 years

4. 811 years

The mass of a proton is 1.0073 u and that of the neutron is 1.0087 u (u = atomic mass unit) The binding energy of ${}_{2}H{e}^4$ is (mass of helium nucleus = 4.0015 u)

1. 28.4 MeV

2. 0.061 u

3. 0.0305 J

4. 0.0305 erg

The binding energies of the nuclei A and B are $E_a and E_b$ respectively. Three atoms of the element B fuse to give one atom of element A and an energy Q is released. Then $E_a, E_b$ and Q are related as:

1. $E_a-3E_b=Q$ 

2. $3E_b-E_a=Q$

3. $E_a+3E_b=Q$ 

4. $E_b+3E_a=Q$

A free neutron decays into a proton, an electron and:

1. A beta particle.

2. An alpha particle.

3. An antineutrino.

4. A neutrino.

In a radioactive sample the fraction of initial number of radioactive nuclei, which remains undecayed after n mean lives is:

1. $\frac{1}{e^n}$ 

2.  $e^n$   

3. $1-\frac{1}{e^n}$ 

4. ${\left(\frac{1}{e-1}\right)}^n$

A nucleus ${}_n{}^{m}X$ emits one $\alpha$ and two $\beta -$particles. The resulting nucleus is

1. ${}_n{}^{m-4}X$ 

2. ${}_{n-2}{}^{m-4}X$   

3. ${}_{n-4}{}^{m-4}X$ 

4. None of these

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

$m_P$ and $m_n$ are masses of proton and neutron respectively. An element of mass m has Z protons and N neutrons, then 

1. $m>Z{m}_p+N{m}_n$

2. $m=Z{m}_p+N{m}_n$

3. $m<Z{m}_p+N{m}_n$

4. m may be greater than, less than or equal to $Z{m}_p+N{m}_n$, depending on the nature of the element.