Energy released in Nuclear fission

Nuclear fission

In 1939, German scientists Otto Hahn and F. Strassman discovered that when uranium nucleus is bombarded with a neutron, it breaks up into two fragments of comparable masses with the release of energy.

The process of breaking up of the nucleus of a heavier atom into two fragments with the release of large amount of energy is called nuclear fission. The fission is accompanied of the release of neutrons. The fission reactions with ₉₂U²³⁵ are represented as

₉₂U²³⁵ + ₀n¹ → ₅₆Ba¹⁴¹ + ₃₆Kr⁹² + 3 ₀n¹ + Q  ………. (1)

₉₂U²³⁵ + ₀n¹ → ₅₄Xe¹⁴⁰ + ₃₈Sr⁹⁴ + 2 ₀n¹ + Q ...(2)

In the above examples the fission reaction is taking place with the release of 3 neutrons and 2 neutrons. On an average 2.5 neutrons per fission are actually released. Of the many possible fission reactions of ₉₂U²³⁵, the reaction given in equation (1) is the most favourable.

Energy released in fission

Let  us  calculate  the  amount  of  energy  released  during  the  fission of ₉₂U²³⁵ with a neutron. The fission reaction is

₉₂U²³⁵ + ₀n¹ → ₅₆Ba¹⁴¹ + ₃₆Kr⁹² + 3₀n¹ + Q

Mass of  ₉₂U²³⁵ = 235.045733 amu

Mass of ₀n¹ = 1.008665 amu

Total mass of the reactant = 236.054398 amu

Mass of ₅₆Ba¹⁴¹ = 140.9177 amu

Mass of ₃₆Kr⁹² = 91.8854 amu

Mass of 3 neutrons = 3.025995 amu

(3 × 1.008665)

Total mass of the products = 235.829095 amu

∴ Mass defect = 236.054398 - 235.829095 = 0.225303 amu

As, 1 amu = 931 MeV, energy released in a fission =

0.225303 × 931 =  200 MeV

Niels Bohr and John A. Wheeler explained the nuclear fission process with the help of liquid drop model. A liquid drop has a spherical shape due to surface tension. On applying external force the sphere changes into ellipsoid, which may change into a dumb bell shape when the force is larger. This may break at the narrow end into two portions.

In the same way, when the heavier nucleus absorbs a neutron, a compound nucleus is formed and is left in an excited state. The excitation energy sets up a series of rapid oscillations. The compound nucleus undergoes distortion from spherical to dumb bell shape. Each portion of the dumb bell has a positive charge and one repels the other. This results in fission and the formation of fission fragments (Fig).