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. ${\left(\frac{1}{e-1}\right)}^n$

The activity of a radioactive sample is measured as 9750 counts/min at t = 0 and as 975 counts/min at t = 5 min. The decay constant is approximately:

1. 0.922/min           

2. 0.691/min         

3. 0.461/min           

4. 0.230/min

Solar energy is due to:

At time t = 0, N₁ nuclei of decay constant λ₁ and N₂ nuclei of decay constant λ₂ are mixed. The decay rate of the mixture is:

1. $-N_1{N}_2{e}^{-\left({\lambda }_1+{\lambda }_2\right)t}$ $$

2. $-\left(\frac{N_1}{N_2}\right)$ $e^{{}^{-\left({\lambda }_1+{\lambda }_2\right)t}}$ $$

3. $-\left(N_1{\lambda }_1{e}^{-{\lambda }_{1}t}\right)$ $+$ $N_2{\lambda }_2{e}^{-{\lambda }_{2}t}$ $$

4. $-N_1{\lambda }_1{N}_2{\lambda }_2{e}^{{}^{-\left({\lambda }_1+{\lambda }_2\right)t}}$