Difficult Questions

## Nuclei

- Are you well prepared? Practice hard questions to be more confident about the chapter
1
Does gamma decay obey conservation of energy? If yes, then what do you think should be the recoil energy of nucleus undergoing gamma decay?
A free nucleus of mass emits a gamma photon (when initially at rest). The energy of the photon is . The recoil energy of the nucleus in is
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2
In beta plus decay, parent nucleus decays into a daughter nucleus along with the emission of a positron neutrino pair. If the energy released in the reaction appears as kinetic energy of the products, which product carried the maximum kinetic energy?
The radio nuclide decays according to

The maximum energy of the emitted positron is
Given the mass values:
and
Calculate and compare it with the maximum energy of the positron emitted.
3
In spontaneous alpha decay, how is the kinetic energy of alpha particle related to the Q value of the reaction?
A nucleus with mass number initially at rest emits an . If the value of the reaction is , calculate the kinetic energy of the
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4
If a radioactive sample is undergoing multiple decay schemes, can you determine the ratio of the parent and daughter nuclei at any given time?
In a radioactive sample nuclei either decay into stable nuclei with decay constant per year or into stable nuclei with decay constant per year. Given that in this sample all the stable and nuclei are produced by the nuclei only. In time years, if the ratio of the sum of stable and nuclei to the radioactive nuclei is , the value of t will be? [Given: In ]
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5
If one fissile U-235 nucleus generates about 200MeV energy, how much uranium do you think you would need to run a nuclear reactor?
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 .
6
If a radioactive sample decays using multiple decay schemes with different half-lives, what do you think should be the effective half-life of the entire sample?
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
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7
In thermonuclear fusion the reacting nuclei need to have enough energy to overcome the coulomb barrier. How can you determine the minimum energy required for the fusion to occur?
Consider the D-T reaction (deuterium-tritium fusion)

Consider the radius of both deuterium and tritium to be approximately . What is the kinetic energy need to overcome the coulomb repulsion between the two nuclei? To what temperature must the gas be heated to initiate the reaction? (Hint: Kinetic energy required for one fusion even = average thermal kinetic energy available with the interacting particles ; Boltzman's constant; absolute temperature