Nuclear Fission

Very large nuclei having mass number greater than 230 tend to be unstable and can split into two or more parts. This is called Fission. Fission process is not a spontaneous one. It occurs when a neutron strikes an unstable nucleus.

In this case, the Uranium 235 will split into two nearly equal nuclei Barium-141 and Krypton-92 and release several free neutrons with huge amounts of energy.

₉₂U²³⁵ + ₀n¹ → ₅₆Ba¹⁴¹ + ₃₆Kr⁹² + 3 ₀n¹ + Energy

₉₂U²³⁵ + ₀n¹ → ₅₄Xe¹⁴⁰ + ₃₈Sr⁹⁴ + 2 ₀n¹ + Energy

These nuclei are isotopes of more stable elements. If left alone, they decay radioactively by emitting alpha or beta particles. The below figure clearly explain how the chain reaction takes place. Out come neutrons from fission process interact with fissile fuel present in the surrounding. Further this reaction produces totally nine neutrons. This cycle repeats to give a reaction.  Moderator like graphite, heavy water and beryllium are used to control the rate of reaction. If the chain reaction is not controlled, a nuclear explosion will occur.

CALCULATING  ENERGY RELEASED BY FISSION

Calculate the energy released in the following spontaneous fission reaction:

²³⁸U → ⁹⁵Sr + ¹⁴⁰Xe + 3n

given the atomic masses to be m(²³⁸U) = 238.050784 u, m(⁹⁵Sr) = 94.919388 u, m(¹⁴⁰Xe) = 139.921610 u, and m(n) =1.008665 u.

Solution

 The products have a total mass of

m_products = 94.919388 u+139.921610 u+3(1.008665 u) = 237.866993 u

The mass lost is the mass of ²³⁸U minus m_products, or

Δm = 238.050784 u − 237.8669933 u = 0.183791 u

so the energy released is E = (Δm) c² = 171.2 MeV

Energy released by 1 Kg of uranium:

Number of atoms in 1 kg of uranium = (6.023 × 10²⁶)/235

Energy released in one fission = 200 MeV

Energy produced by 1 kg of uranium during fission

E = (6.023 × 10²⁶ × 200)/235 = 5.128 × 10²⁶ MeV

E = (5.128 × 10²⁶) × (1.6×10^-13) J      [1 MeV = 1.6×10^-13 J]

E = {(5.128 × 10²⁶) × (1.6×10^-13)}/{3.6× 10⁶} k Wh

E = 2.26 × 10⁷ k Wh                                    [1k Wh = 3.6×10⁶ J]

Due to this reason, nuclear energy is being used for the generation of electricity. 

Most of the energy that is released during fission goes into the K.E of the fission fragments. The emitted neutrons, Beta and gamma rays and neutrinos carry off perhaps 20% of the total energy.

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