If the nuclear density of the material of atomic mass 27 is \(3\rho _{0},\)$t$hen the nuclear density of the material of atomic mass 125 is:

1.  5${\rho }_0$

2.  3${\rho }_0$

3.  $\frac{5}{3}$${\rho }_0$

4.  ${\rho }_0$

A radioactive sample has a half-life of 1770 years. At some instant, 20% of the sample has decayed. If taking this instant as $t$ $=$ $t_1$, it is found that at $t$ $=$ $t_2$, 20% of the sample is left, then $t_2$ $-$ $t_1$ is:

1.  1770 years

2.  885 years

3.  2655 years

4.  3540 years 

If the half-life of a radioactive substance is 10 hours, then its mean life is:

1.  14.4 h

2.  7.2 h

3.  20 h

4.  6.93 h

${}_8{}^{19}\mathrm{O}$ $\to$ ${}_9{}^{19}\mathrm{F}$ $+$ $\mathrm{A}$ $+$ $\mathrm{B}$

In the given decay equation, A and B indicate:

After two alpha decays and four beta(-ve) decays, the atomic number:

Binding energy per nucleon of a fixed nucleus ^A$X$ is 8 MeV. It absorbs a neutron moving with kinetic energy 4 MeV and converts into Y emitting a photon of energy 2 MeV. The binding energy per nucleon of Y (in MeV) is:

1.  $\frac{8A+2}{A+1}$

2.  $\frac{8A-2}{A+1}$

3.  $\frac{8A-1}{A+1}$

4.  $\frac{8A}{A+1}$

The statement which is incorrect about nuclear force between two protons is?

The volume (V) of a nucleus is related to its mass (M) as:

1.  $V$ $\propto$ $M$

2.  $V$ $\propto$ $\frac{1}{M}$

3.  $V$ $\propto$ $M^3$

4.  $V$ $\propto$ $\frac{1}{M^3}$

A sample of radioactive material has initial mass A, decay constant B, molecular weight C and Avogadro's constant D. The activity of the sample after time, t, will be:

1.  $\left(\frac{AD}{C}\right)e^{-BT}$

2.  $\left(\frac{AD}{CB}\right)e^{-BT}$

3.  $\left(\frac{ADB}{C}\right)e^{-BT}$

4.  $\left(\frac{ADC}{B}\right)e^{-BT}$

If the density of gold nucleus is X, then the density of silver nucleus will be:

1.  2X

2. $\frac{X}{3}$

3.  4X

4.  X