When an \(\alpha\text-\) 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. \(\frac{1}{\sqrt{m}}\)
2. \(\frac{1}{m^2}\)
3. \(m\)
4. \(\frac{1}{m}\)

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

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.  $10 \mathrm{\mu g}$

The half-life of a radioactive element X is 50 yrs. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio of 1:15 in a sample of a given rock. The age of the rock was estimated to be:

1.  200 yr

2.  250 yr

3.  100 yr

4.  150 yr