Q.Write the nuclear reaction of $^{235}_{92}U$ bombarded with a slow neutron. Calculate the energy released in KWh in the fission of 50 kg of $^{235}_{92}U$. OR Using Bohr's quantization condition for angular momentum of an electron revolving around the hydrogen nucleus, establish the expression of the radius of the stationary orbits of hydrogen atom.

Fission splits a heavy nucleus (easy to trigger); fusion joins light nuclei (needs extreme heat to overcome Coulomb repulsion).

Nuclear fission is the splitting of a single heavy nucleus (e.g. uranium-235) into two lighter fragments, which can be triggered at ordinary temperatures/conditions, for example by the absorption of a slow (thermal) neutron. Nuclear fusion, on the other hand, is the combining of two light nuclei (e.g. hydrogen isotopes) into a heavier nucleus; because both nuclei are positively charged and repel each other strongly, fusion requires extremely high temperatures (of the order of $10^7$–$10^8$ K, as found in stellar cores) to give the nuclei enough kinetic energy to …

A moderator slows fast neutrons to thermal speeds so they are more readily captured for fission.

Fission of $^{235}$U releases fast neutrons (~2 MeV). These fast neutrons have a low probability of causing further fission. A moderator (heavy water, graphite, or ordinary water) contains light nuclei that slow the neutrons down by repeated elastic collisions, bringing them to thermal energies (~0.025 eV), where t …

BARC, India's premier nuclear research institute, is situated at Trombay in Mumbai.

The Bhabha Atomic Research Centre (BARC) was established in 1954 by Dr. Homi J. Bhabha (originally as the Atomic Energy Establishment, Trombay) and renamed BARC in 1967 in his honour. It is India's largest nuclear research facility, working on nuclear reactor technology, radioisotope production and …

Nuclear fission is the splitting of a heavy nucleus into two medium-mass nuclei with release of neutrons and energy, illustrated by the classic $^{235}$U fission reaction.

Solution:

Nuclear fission is the nuclear reaction in which a heavy nucleus (such as $^{235}_{92}\text{U}$), on absorbing a slow (thermal) neutron, splits into two nuclei of roughly comparable (medium) mass, along with the emission of two or three fast neutrons and a large amount of energy (since the binding energy per nucleon of the fragments is higher than that of the parent nucleus).

A typical fission reaction:

${}_{92}^{235}\text{U} + {}_{0}^{1}n \longrightarrow {}_{56}^{144}\text{Ba} + {}_{36}^{89}\text{Kr} + 3\,{}_{0}^{1}n + Q$

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An atom bomb releases energy by splitting heavy nuclei (nuclear fission), not by fusing light nuclei.

An atom bomb (fission bomb) works by an uncontrolled chain reaction of nuclear fission: a heavy, fissile nucleus such as $^{235}_{92}\text{U}$ or $^{239}_{94}\text{Pu}$ absorbs a neutron, becomes unstable, and splits into two lighter nuclei plus 2–3 fast neutrons, releasing a large amount of energy (from the mass defect, via $E=\Delta m c^2$). Each released neutron can trigger further fissions in nearby nuclei, causing a rapidly multiplying, uncontrolled chain reaction tha …

A moderator slows down fast neutrons released in fission to thermal energies (needed to sustain the chain reaction) via elastic collisions; heavy water (and graphite) do this efficiently while absorbing very few neutrons.

In a nuclear (fission) reactor, neutrons released by fission of $^{235}\text{U}$ are fast (high energy, ~MeV), but the fission cross-section is much larger for slow (thermal) neutrons. A moderator's job is to slow these fast neutrons down through repeated elastic collisions. Energy transfer per collision is maximum when the target nucleus has a mass close to that of the neutron, so light nuclei (hydrogen, deuterium, carbon) make good moderators — and, crucially, they must also have a low neutron-absorption cross-section so they don't remove neutrons from the chain reaction. …

The coolant's job is to remove the enormous heat produced by fission in the reactor core and transport it out safely and usefully.

In a nuclear reactor, the controlled fission chain reaction in the fuel rods releases a large amount of thermal energy. A coolant (such as water, heavy water, liquid sodium, or a gas like CO$_2$/helium, depending on reactor design) is circulated through the reactor core.

Functions of the coolant:

1. It absorbs the heat generated in the core by flowing past the fuel rods.
2. It transports this heat out of the reactor core to a heat exchanger/steam generator, where the heat is used to convert water into high-pressure steam.
3. This steam then drives a turbine coupled to a generator, producing electricity. …

An atom bomb releases its energy through an uncontrolled chain of nuclear fission reactions.

When a heavy nucleus such as $U^{235}$ or $Pu^{239}$ absorbs a neutron, it splits (fission) into two lighter nuclei, releasing energy and 2-3 more neutrons. If the multiplication factor $k>1$ and nothing limits the reaction, these neutrons trigger further fissions in an exponentially growing, uncontrolled chain reaction, releasing an enormous amount of energy in a fraction of a second — an explosion. This is exactly the mechanism of an atom bomb.

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