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

The beta particles of a radioactive metal originate from:

1.  The free electrons in the metal

2.  The orbiting electrons of the metal atoms

3.  The photons released from the nucleus

4.  The nucleus of the metal atoms

The isotope Cobalt-57 has a half-life of 272 days. How long does it take for this isotope to decay to about one-sixteenth of its original amount?

1.  544 days

2.  1088 days

3.  1128 days

4.  2176 days