A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2 : 1. The ratio of their nuclear size will be

• 2^1/3 : 1

• 1 : 3^1/2

• 3^1/2 : 1

• 1 : 2^1/2

A block having 12g of element is placed in a room. This element is a radioactive element with half-life of 15 yr. After how many years will there be just 1.5 g of the element in the box?

• 40 yr

• 45 yr

• 20 yr

• 15 yr

A⁷ Li target is bombarded with a proton beam current of 10^-4 A for one hour to produce ⁷Be of activity 1.8 × 10⁸ disintegrations per second. Assuming that one ⁷Be radioactive nuclei is produced by bombarding 1000 protons, its half-life is

• 0.87 × 10⁷ s

• 0.2 × 10⁷ s

• 0.67 × 10⁸ s

• 0.87 × 10⁶ s

Two radioactive materials X₁ and X₂ have decay constants 6 and 3A respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X₁ to that of X₂ will be $\frac{1}{\mathrm{e}}$  after a time

• $\frac{1}{6 \mathrm{\lambda }}$

• $\frac{1}{3 \mathrm{\lambda }}$

• $\frac{3}{6 \mathrm{\lambda }}$

• $\frac{6}{9 \mathrm{\lambda }}$

A neutron in a nuclear reactor collides head on elastically with the nucleus of a carbon atom initially at rest. The fraction of kinetic energy transferred from the neutron to the carbon atom is

• $\frac{11}{12}$

• $\frac{2}{11}$

• $\frac{48}{121}$

• $\frac{48}{169}$

Assertion: Thermonuclear fusion reactions may become the source of unlimited power for the mankind.

Reason: A single fusion event involving isotopes of hydrogen produces more energy from nuclear fission of  ${}_{93}{}^{235}\mathrm{U}$

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

An atom of mass number 15 and atomic number 7 captures an a-particle and then emits a proton. The mass number and atomic number of the resulting atom will be respectively

• 14 and 12

• 15 and 3

• 16 and 4

• 18 and 8

A zener diode is specified as having a breakdown voltage of 9.1 V, with a maximum power dissipation of 364 mW. What is the maximum current the diode can handle?

• 40 mA

• 60 mA

• 50 mA

• 45 mA

Assertion: Generally heavy nuclei are unstable.

Reason: It has more neutrons and protons.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false

The half-life of radium is 1600 years. What is the fraction of sample undecayed after 6400 years?

• $\frac{1}{16}$

• $\frac{1}{4}$

• $\frac{1}{8}$

• $\frac{1}{24}$