In radioactive decay process, the negatively charged emitted β-particles are:

1. the electrons present inside the nucleus

2. the electrons produced as a result of the decay of neutrons inside the nucleus

3. the electrons produced as a result of collisions between atoms

4. the electrons orbiting around the nucleus

A nucleus ${}_Z{X}^A$ has mass represented by M(A, Z). If M_p and M_n denote the mass of proton and neutron respectively and BE the binding energy, then :

1. $BE=\left[M\right(A,Z)-Z{M}_p-(A-Z\left)M_n\right]c^2$

2. $BE=[Z{M}_p+(A-Z)M_n-M(A, Z\left)\right]c^2$

3. $BE=[Z{M}_p+A{M}_n-M-(A, Z\left)\right]c^2$

4. $BE=M(A, Z)-Z{M}_p-(A-Z)M_n$

Two radioactive substances A and B have decay constants 5λ and λ respectively. At t = 0 they have the same number of nuclei. The ratio of the number of nuclei of A to those of B will be $\frac{1}{e^2}$ after a time interval:

1. $\frac{1}{4\lambda }$

2. $4\lambda$

3. $2\lambda$

4. $\frac{1}{2\lambda }$

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