Nuclei

What is the particle X in the following nuclear reaction ?

    ${}_4{}^9\mathrm{Be} + {}_2{}^4\mathrm{He} \stackrel{}{\to } {}_6{}^{12}\mathrm{C} + \mathrm{X}$

• Electron

• Proton

• Photon

• Neutron

At time t = O, a radioactive sample has a mass of 10 g. Calculate the expected mass of radioactive sample after two successive mean lives.

The energy released by the fission of one uranium atom is 200 MeV. The number of fissions per second required to produce 3.2 W of power is (Take, 1eV = 1.6 x 10^-19 J)

• 10⁷

• 10¹⁰

• 10¹⁵

• 10¹¹

A radioactive isotope X with half life 1.5x 10⁹ yr decays into a stable nucleus Y. A rock sample contains both elements X and Y in ratio 1 : 15. Find the age of the rock.

A radioactive nucleus of mass number A, initially at rest, emits an α-particle with a speed v. The recoil speed of the daughter nucleus will be

• $\frac{2\mathrm{v}}{\mathrm{A} - 4}$

• $\frac{2\mathrm{v}}{\mathrm{A} + 4}$

• $\frac{4\mathrm{v}}{\mathrm{A} - 4}$

• $\frac{4\mathrm{v}}{\mathrm{A} + 4}$

In the nuclear reaction ${}_7{}^{14}\mathrm{N} + \mathrm{X} \underset{}{\to } {}_6{}^{14}\mathrm{C} + {}_1{}^1\mathrm{H}$, the X will be

• ${}_{-1}{}^0\mathrm{e}$

• ${}_1{}^1\mathrm{H}$

• ${}_1{}^2\mathrm{H}$

• ${}_0{}^1\mathrm{n}$

Two radioactive substances A and B have decay constants 5 λ and λ respectively. At t = 0, they have the same number of nuclei. The ratio of number of nuclei of A to that of B will be (1/e)² after a time interval of

• $\frac{1}{\mathrm{\lambda }}$

• $\frac{1}{2\mathrm{\lambda }}$

• $\frac{1}{3\mathrm{\lambda }}$

• $\frac{1}{4\mathrm{\lambda }}$

The half-life of a radioactive isotope X is 20 yr. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be

• 40 yr

• 60 yr

• 80 yr

• 100 yr

A certain mass of hydrogen is changed to helium by the process of fusion. The mass defect in fusion reaction is 0.02866 u. The energy liberated per u is (given 1 u = 931 MeV)

• 2.67 MeV

• 26.7 MeV

• 6.675 MeV

• 13.35 MeV

For the radioactive nuclei that undergo either α or β decay, which one of the following cannot occur ?

• Isobar of original nucleus is produced

• Isotope of the original nucleus is produced

• Nuclei with higher atomic number than that of the original nucleus is produced

• Nuclei with lower atomic number than that of the original nucleus is produced