Calculate the radius of the earth if the density of the earth is equal to the density of the nucleus.[mass of earth 5.97 x 10²⁴ kg].

Half lives of two radioactive elements A and B are 20 minutes and 40 minutes respectively. Initially, the samples have equal number of nuclei. Calculate the ratio of decayed numbers of A and B nuclei after 80 minutes.

Calculate the time required for 60% of a sample of radon undergo decay. Given T_1/2 of radon = 3.8 days.

Show that the mass of radium \((_{ 88 }^{ 226 }{ Ra })\) with an activity of 1 curie is almost a gram. Given T_1/2 = 1600 years.

Compute the binding energy of  \(_{ 2 }^{ 4 }{ He }\) nucleus using the following data: Atomic mass of Helium atom M_A(He) = 4.00260u and that of hydrogen atom, m_H = 1.00785u.