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A $1000MW$ fission reactor consumes half of its fuel in $5.00y$. How much $_{92}U$ did it contain initially? Assume that the reactor operates $80%$ of the time, that all the energy generated arises from the fission of $_{92}U$ and that this nuclide is consumed only by the fission process.

For the $β_{+}$ (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)

$e_{+}+_{Z}X→_{Z−1}Y+v$

Show that if $β_{+}$ emission is energetically allowed, electron capture is necessarily allowed but not vice-versa

$e_{+}+_{Z}X→_{Z−1}Y+v$

Show that if $β_{+}$ emission is energetically allowed, electron capture is necessarily allowed but not vice-versa

A source contains two phosphorous radio nuclides $_{15}P(T_{1/2}=14.3d)$ and $_{15}P(T_{1/2}=25.3d)$. Initially, 10% of the decays come from $_{15}P$. How long one must wait until 90% to do so?

(a)Calculate the energy released if $_{238}U$ emits an $α$-particle.

(b) Calculate the energy supplied to $_{238}U$ if two protons and two neutrons are to be emitted one by one. The atomic masses of $_{238}U$, $_{234}Th$ and $_{4}He$ are $238.0508u,234.04363u$ and $4.00260u$ respectively.

Suppose India had a target of producing by $2020AD,200000$$MW$ of electric power, $10$ $%$ 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 $25$ $%$ How much amount of fissionable uranium would our country need per year by $2020$ $?$ Take $235$ $U$ to be about $200$ $MeV$ .

A radioactive sample can decay by two different processes. The half-life for the first process is $T_{1}$ and that for the second process is $T_{2}$. The effective half-life $T$ 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 $_{96}Cm$ has a mean-life of $10_{13}s$. Its primary decay modes are spontaneous fission and $α−decay$, 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 $α−decay$ are as follows:

$_{98}Cm=248.07220u,_{94}Pu=244.064100u$, and $_{2}He=4.002603u$.

Calculate the power output from a sample of $10_{20}Cm$ atoms. $(1u=931MeVc_{−2})$

$_{98}Cm=248.07220u,_{94}Pu=244.064100u$, and $_{2}He=4.002603u$.

Calculate the power output from a sample of $10_{20}Cm$ atoms. $(1u=931MeVc_{−2})$