# Question ad2f5

May 25, 2017

U-235 fission => intermediate weight nuclei with higher (stronger) binding energies.

#### Explanation:

The general equation for fission of U- 235 is

U-235 + neutron => U-236 => Ba-144 + Kr-89 + 3 neutrons + Binding Energy (Other intermediate weight nuclei are also formed, but this is just for this illustration.)

Binding Energy is the energy released on formation of specified nuclei. Binding Energy is typically measured in electron volts (eV) where MeV is Megaelectronvolts ( = 1.6022E-16 Kilojoules) .

The binding energy of U-235 = 7.56 MeV/nucleon
The binding energy of Ba-144= 8.26 MeV/nucleon

(BE U-235) - (BE Ba-144) = 7.56 - 8.26 MeV/nucleon = - 0.70 MeV/nucleon

Converting to Kj/nucleon:
=> - 0.70 MeV/nucleon ( 1.6022E-16 Kj/MeV ) = - 1.1215E-16 Kj/nucleon

Converting to Kj/mole:
=> - 1.1215E-16 Kj/nucleon (6.023E+23 nucleons/mole) = - 6.8E+07 Kj/mole

NOTE: The Heat of Combustion of candle wax is ~ 1.3E+04 Kj/mole*. Nuclear fission gives ~ 5000 times more energy per mole.

May 25, 2017

The fission products have less mass than the reactants, and this mass defect is converted into energy.

#### Explanation:

A typical equation for nuclear fission is

$\text{_0^1"n" +color(white)(l) _92^235"U" →color(white)(l) _56^141"Ba" +color(white)(l) _36^92"Kr" + 3_0^1"n}$

Calculate the mass of the reactants

$\text{_0^1"n" +color(white)(l) _92^235"U" = ‎"1.0087 u + 235.0439 u" ="236.0526 u}$

Calculate the mass of the products

$\text{ _56^141"Ba" +color(white)(l) _36^92"Kr" + 3_0^1"n" = "140.9144 u + 91.9262 u + 3.0260 u = 235.8666 u}$

Calculate the mass defect

$\text{Mass defect" = "236.0526 u - 235.8666 u" = "0.1860 u}$

Convert the mass defect to energy

0.1860 color(red)(cancel(color(black)("u"))) × (1.6605 × 10^"-27"color(white)(l) "kg")/(1 color(red)(cancel(color(black)("u")))) = "3.0885 × 10"^"-28"color(white)(l) "kg"

$E = m {c}^{2} = \text{3.0885 × 10"^"-28"color(white)(l) "kg" × ("2.9979 × 10"^8color(white)(l) "m·s"^"-1")^2 = "2.7758 × 10"^"-11"color(white)(l) "J}$

This is the energy released by the fission of one atom of uranium-235.

The energy released by one gram of uranium-235 is

1 color(red)(cancel(color(black)("g U"))) × (1 color(red)(cancel(color(black)("mol U"))))/("235.0439" color(red)(cancel(color(black)("g U")))) × (6.022 × 10^23 color(red)(cancel(color(black)("atoms U"))))/(1 color(red)(cancel(color(black)("mol U")))) × ("2.7758 × 10"^"-11"color(white)(l) "J")/(1 color(red)(cancel(color(black)("atom U"))))

= 7.1112 × 10^10 color(white)(l)"J" = 71.112 × 10^6color(white)(l) "kJ"#

In contrast, the energy released by burning 1 g of paraffin wax is 42.0 kJ/g.

The fission of 1 g of uranium-235 releases nearly two million times the energy as the combustion of 1 g of paraffin wax.