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Fission | Physics

Hundreds of nuclear fission power plants around the world attest to the fact that ... Fission is the opposite of fusion and releases energy only when heavy nuclei are split. ... The amount of energy per fission reaction can be large, even by nuclear ... Calculate the energy released in the following spontaneous fission reaction:.

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Given that

Power P = 100 W  

Mass of the deuterium = 2.0 kg

Nuclear reaction: ^{2}_1 H + ^{2}_1 H \rightarrow ^{3}_{2} He + n + 3.27   MeV  

Step 1: Finding the number of atoms in the 2 kg fission matter

Avogadro number NA = 6.023 * 10^{23}

Atomic mass of deuterium =\ 2

Mass of a deuterium m=2\ kg\ =\ 2000\ g 

Number of atoms in the 2kg deuterium,\ N=\frac{NA}{A}*m

= \frac{6.023*10^{23}}{2}* 2 kg   

= 6.023*10^{26} atoms

Step 2: Determining the total energy released during the fission of atoms in 2kg

For two deuterium under fusion release 3.27 MeV

Average energy per fission = \frac{3.27}{2} = 1.635     

Total energy E = Average energy per fusion * Number of atoms

E = 1.635 * 6.023*10^{26}

E = 9.85* 10^{26} MeV

E = 9.85* 10^{26} * 1.6* 10^{-19} * 10^{6}  Joules

E = 1.576 * 10^{14}   Joules

Step 3: Detecting the length(time) of an electric lamp's glow

The amount of energy divided by the time equals power.

P = \frac{E}{t}

t = \frac{E}{P}

t = \frac{ 1.576 * 10^{14}}{100}   

t = 1.576 * 10^{12} seconds

t = \frac{1.576 * 10^{12}}{365* 60*60* 24}

t = 4.9 * 10^{4} years

Hence, The amount of time it takes for the lamp to glow t = 4.9 * 10^{4} years