Difficult Conceptual Numericals
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- Solve the toughest problems
A  fission reactor consumes half of its fuel in . How much  did it contain initially? Assume that the reactor operates  of the time, that all the energy generated arises from the fission of  and that this nuclide is consumed only by the fission process.
For the (positron) emission from a nucleus, there is another competing process known as electron capture (electron from an inner orbit, say, the K-shell, is captured by the nucleus and a neutrino is emitted)

Show that if emission is energetically allowed, electron capture is necessarily allowed but not vice-versa
A source contains two phosphorous radio nuclides and . Initially, 10% of the decays come from . How long one must wait until 90% to do so?
(a)Calculate the energy released if emits an -particle.
(b) Calculate the energy supplied to  if two protons and two neutrons are to be emitted one by one. The atomic masses of , and are and respectively.
Suppose India had a target of producing by  of electric power, of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilisation (i.e.conversion to electric energy) of thermal energy produced in a reactor was How much amount of fissionable uranium would our country need per year by  Take to be about .
A radioactive sample can decay by two different processes. The half-life for the first process is and that for the second process is . The effective half-life of the radioactive sample is
When an alpha particle collides elastically with a nucleus, the nucleus recoils. Suppose a 5.00 MeV alpha particle has a head on elastic collision with a gold nucleus that is initially at rest. What is the kinetic energy of (a) the recoiling nucleus and (b) the rebounding alpha particle?
The element curium has a mean-life of . Its primary decay modes are spontaneous fission and , the former with a probability of 8% and the latter with a probability of 92%. Each fission releases 200 MeV energy. The masses involved in are as follows:
, and .
Calculate the power output from a sample of atoms.