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

Consider the following nuclear reactions:

$\mathrm{I}.{}_7^{14}\mathrm{N}{+}_2^4\mathrm{He}{\to }_8^{17}\mathrm{O}+\mathrm{X}$
$\mathrm{II}.{}_4^9\mathrm{Be}{+}_2^4\mathrm{H}{\to }_6^{12}\mathrm{He}+\mathrm{Y}$

Then :

1.  X and Y are both protons.

2.  X and Y are both neutrons.

3.  X is a proton and Y is a neutron

4.  X is a neutron and Y is a proton

A nucleus of lead ${\mathrm{Pb}}_{82}^{214}$ emits two-electron followed by an alpha particle. The resulting nucleus will have:

1.  82 protons and 128 neutrons

2.  80 protons and 130 neutrons

3.  82 protons and 130 neutrons

4.  78 protons and 134 neutrons

Consider the following statements:

(I) All isotopes of elements have the same number of neutrons.

(II) Only one isotope of an element can be stable and non-radioactive.

(Ill) All elements have isotopes.

(IV) All isotopes of Carbon can form chemical compounds with Oxygen-16.

The correct option regarding an isotope is-

1.  III and IV only

2.  II, III, and IV only

3.  I, II, and III only

4.  I, III, and IV only