A radioactive element  ${}_{90}\mathrm{X}^{238}$ decays into ${}_{83}\mathrm{Y}^{ 222}$. The number of β-particles emitted are 

• 1

• 2

• 4

• 6

The binding energy per nucleon is maximum in the case

• ${}_{92}{}^{235}\mathrm{U}$

• ${}_{56}{}^{141}\mathrm{Ba}$

• ${}_{26}{}^{56}\mathrm{Fe}$

• ${}_4{}^2\mathrm{He}$

The half-life of radio isotope is 4 h. If initial mass of the isotope was 200 g, then mass remaining after 24 h will be

• 1.042 g 

• 2.084 g

• 3.125 g

• 4.167 g

Remaining quantity (in%) of radioactive element after 5 half lives is

• 4.125%

• 3.125%

• 31.1%

• 42.125%

The half-life of ¹⁹⁸Au is 2.7 days. The average life is

• 4 days

• 3.4 days

• 3.9 days

• None of the above

If M_O is the mass of an oxygen isotope ₈O¹⁷ M_p and M_n are the masses of a proton and a neutron, respectively, the nuclear binding energy of the isotope is

• M_O c²

• ( M_O - 17M_n ) c²

• (M_O - 8M_p ) c²

• ( 8 M_p + 9 M_n - M_O)

67.

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

• $\frac{1}{6 \mathrm{\lambda }}$

• $\frac{1}{3 \mathrm{\lambda }}$

• $\frac{3}{6 \mathrm{\lambda }}$

• $\frac{6}{9 \mathrm{\lambda }}$