# What is the respective number of $\alpha$ and $\beta$-particles emitted in the following radioactive decay?   1. 6 and 8 3. 6 and 6 3. 8 and 8 4. 8 and 6

Subtopic:  Types of Decay |
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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

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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

Subtopic:  Mass-Energy Equivalent |
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The binding energies of the nuclei A and B are  respectively. Three atoms of the element B fuse to give one atom of element A and an energy Q is released. Then  and Q are related as:

1. ${E}_{a}-3{E}_{b}=Q$

2. $3{E}_{b}-{E}_{a}=Q$

3. ${E}_{a}+3{E}_{b}=Q$

4. ${E}_{b}+3{E}_{a}=Q$

Subtopic:  Nuclear Binding Energy |
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A free neutron decays into a proton, an electron and:

1. A beta particle.

2. An alpha particle.

3. An antineutrino.

4. A neutrino.

Subtopic:  Types of Decay |
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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. ${\left(\frac{1}{e-1}\right)}^{n}$

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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

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The energy equivalent of one atomic mass unit is:

1. $1.6×{10}^{-19}$ $J$

2. $6.02×{10}^{23}$ $J$

3. 931 MeV

4. 9.31 MeV

Subtopic:  Mass-Energy Equivalent |
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Solar energy is due to:

1. fusion reaction.

2. fission reaction.

3. combustion reaction.

4. chemical reaction.

Subtopic:  Nuclear Energy |
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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. $-{N}_{1}{\lambda }_{1}{N}_{2}{\lambda }_{2}{e}^{{}^{-\left({\lambda }_{1}+{\lambda }_{2}\right)t}}$