(a) If \(\alpha \)-decay of \(_{ 92 }{ { U }^{ 238 } }\) is energetically allowed (i.e. the decay products have a total mass less than the mass of \(_{ 92 }{ { U }^{ 238 } }\)), what prevents \(_{ 92 }{ { U }^{ 238 } }\) from decaying all at once? Why is its half life so large?
(b) The \(\alpha \)-particle faces a Coulomb barrier. A neutron being uncharged faces no such barrier. Why does the nucleus \(_{ 92 }{ { U }^{ 238 } }\) not decay spontaneously, by emitting a neutron?

The half-lives of radioactive nuclides that emit \(\alpha \)-rays vary from microsecond to billion years. What is the reason for this large variation in the half life of alpha emitters?

There is a stream of neutrons with a kinetic energy of 0.0327 eV. If the half life of neutrons is 700 seconds, what fraction of neutrons will decay before they travel a distance of 10 m? Given mass of neutron \(=1.675\times { 10 }^{ -27 }kg.\)

The radioactive decay rate of a radio active element is found to be \({ 10 }^{ 3 }\) disintegrations/sec. at a certain time. If half life of the element is one second, what would be the decay rate after 1 sec. and after 3 sec.?

The isotopes of \({ U }^{ 238 }\ and\ { U }^{ 235 }\) occur in nature in the ratio 140 : 1. Assuming that at the time of earth's formation, they were present in equal ratio, make an estimate of the age of the earth. The half lives of \({ U }^{ 238 }\ and\ { U }^{ 235 }\) are \(4.5\times { 10 }^{ 9 }\) years and \(7.13\times { 10 }^{ 8 }\) years respectively.
Given : \(\log _{ 10 }{ 140 } =2.1461,\log _{ 10 }{ 2 } =0.3010\)