In a radioactive material, the activity at time t₁ is R₁ and at a later time t₂, it is R₂. If the decay constant of the material is λ, then:

1. $R_1=R_2{e}^{\lambda (t_1\mathit{+}{t}_2)}$

2. $R_1=R_2{e}^{-\lambda (t_1-t_2)}$

3. $R_1=R_2(t_1-t_2)$

4. $R_1=R_2$

The radius of Germanium (Ge) nuclide is measured to be twice the radius of ${}_4{}^9\mathrm{Be}$. The number of nucleons in Ge are:

1. 73

2. 74

3. 75

4. 72

$\alpha$-particle consists of:

1. 2 protons only

2. 2 protons and 2 neutrons only

3, 2 electrons, 2 protons, and 2 neutrons

4. 2 electrons and 4 protons only

Choose the incorrect assertion regarding binding energy per nucleon:

1. Binding energy per nucleon is practically constant for nuclei with mass numbers between 30 and 170.

2. Binding energy per nucleon is maximum for ${}_{56}\mathrm{Fe}$ (equal to 8.75 meV).

3. Binding energy per nucleon for ${}_6\mathrm{Li}$ is lower compared to ${}_4\mathrm{He}$.

4. Higher the binding energy per nucleon, the more unstable is the nucleus.

Which of these is Q-value of ${\mathrm{\beta }}^{+}$ decay of ${}_{11}{}^{22}\mathrm{Na}$ into ${}_{10}{}^{22}\mathrm{Ne}$?

(${\mathrm{m}}_1, {\mathrm{m}}_2, \mathrm{and} {\mathrm{m}}_3$ represent masses of Na-atom, Ne-atom, and electron respectively) 

1.  $({\mathrm{m}}_1 + {\mathrm{m}}_2){\mathrm{c}}^2$

2.  $({\mathrm{m}}_1 + {\mathrm{m}}_2 - 2{\mathrm{m}}_3){\mathrm{c}}^2$

3.  $({\mathrm{m}}_1 - {\mathrm{m}}_2 - {\mathrm{m}}_3){\mathrm{c}}^2$

4.  $({\mathrm{m}}_1 - {\mathrm{m}}_2 - 2{\mathrm{m}}_3){\mathrm{c}}^2$

A sample of radioactive material has mass m, decay constant $\mathrm{\lambda }$ and molecular weight M. Avogadro constant = ${\mathrm{N}}_{\mathrm{A}}$. The initial activity of the sample is:

1.  $\mathrm{\lambda m}$

2.  $\frac{\mathrm{\lambda m}}{\mathrm{M}}$

3.  $\frac{{\mathrm{\lambda mN}}_{\mathrm{A}}}{\mathrm{M}}$

4.  ${\mathrm{mM}}_{\mathrm{A}}{\mathrm{e}}^{\mathrm{\lambda }}$

Consider the information given. Nuclear mass of ${}_{20}{}^{41}\mathrm{Ca}$ = 40.962278 u, nuclear mass of ${}_{20}{}^{40}\mathrm{Ca}$ = 39.962591 u, mass of neutron = 1.00866 u. Neutron separation energy for ${}_{20}{}^{41}\mathrm{Ca}$ is:

1.  7.458 MeV 

2.  8.358 MeV

3.  9.568 MeV

4.  10.008 MeV

Two radioactive materials ${\mathrm{X}}_1 \mathrm{and} {\mathrm{X}}_2$ have decay constant $11\mathrm{\lambda } \mathrm{and} \mathrm{\lambda }$ respectively. If initially, they have the same number of nuclei, then the ratio of the number of nuclei  ${\mathrm{X}}_1 \mathrm{and} {\mathrm{X}}_2$ will be $\frac{1}{{\mathrm{e}}^2}$ after a time:

1.  $\frac{1}{5\mathrm{\lambda }}$

2.  $\frac{1}{11\mathrm{\lambda }}$

3.  $\frac{1}{10\mathrm{\lambda }}$

4.  $\frac{1}{9\mathrm{\lambda }}$

A radioactive nucleus X decays to a stable nucleus Y. Then, the graph of the rate of formation R of Y against time will be:

1.         2.  

3.         4.  

A radioactive sample has a half-life of 30 minutes. At 3 PM, its decay rate was measured as 120,000 counts/s. What will be the decay rate at 5 PM?

1.  120,000 counts/second

2.  60,000 counts/second

3.  30,000 counts/second

4.  7,500 counts/second