For radioactive material, the half-life is 10 minutes. If initially, there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is :

1. 20

2. 10

3. 30

4. 15

When an α– particle of mass m moving with velocity v bombards a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on m as:

1. $\frac{1}{\sqrt{\mathrm{m}}}$

2. $\frac{1}{{\mathrm{m}}^2}$

3. m

4. $\frac{1}{\mathrm{m}}$

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then,

1. The nucleus helium has more kinetic energy than the thorium nucleus

2. The helium nucleus has less momentum than the thorium nucleus

3. The helium nucleus has more momentum than the thorium nucleus

4. The helium nucleus has less kinetic energy than the thorium nucleus

A radioisotope 'X' with a half-life 1.4 × 10⁹ years decays to 'Y' which is stable. A sample of the rock from a cave was found to contain 'X' and 'Y' in the ratio 1:7. The age of the rock is :

1. 1.96 x 10⁹ years

2. 3.92 x 10⁹ years

3. 4.20 x 10⁹ years

4. 8.40 x 10⁹ years

A certain mass of Hydrogen is changed to Helium by the process of fusion. The mass defect in the fusion reaction is 0.02866 u. The energy liberated per nucleon is: (Given 1 u = 931 MeV)

If the nuclear radius of ²⁷Al is 3.6 Fermi, the approximate nuclear radius of ⁶⁴Cu in Fermi is:

1. 2.4

2. 1.2

3. 4.8

4. 3.6

A mixture consists of two radioactive materials A₁ and A₂ with half-lives of 20 s and 10 s respectively. Initially, the mixture has 40 g of A₁ and 160 g of A₂. The amount of the two in the mixture will become equal after:

1. 60 s

2. 80 s

3. 20 s

4. 40 s

The power obtained in a reactor using ${\mathrm{U}}^{235}$disintegration is 1000 kW. The mass decay of ${\mathrm{U}}^{235}$per hour is approximately equal to:

1.  $20 \mathrm{\mu g}$

2. $40 \mathrm{\mu g}$

3.  $1 \mathrm{\mu g}$

4.  $10 \mathrm{\mu g}$