Work, Energy and Power

Estimate the amount of energy released in the nuclear fusion reaction: where Express your answer in units of MeV. - Wired Faculty

Question

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Estimate the amount of energy released in the nuclear fusion reaction:

$straight H presuperscript 2 subscript 1 plus straight H presuperscript 2 subscript 1 rightwards arrow He presuperscript 3 subscript 2 plus straight n$

$straight m left parenthesis straight H presuperscript 2 subscript 1 right parenthesis equals 2.0141 space amu comma space space straight m left parenthesis He presuperscript 3 subscript 2 right parenthesis space equals space 3.0160 space amu comma$

$straight m subscript straight n equals 1.0087 space amu$

where $1 space amu space equals space 1.661 cross times 10 to the power of negative 27 end exponent kg$

Express your answer in units of MeV.

Solution

The given reaction is,

$straight H presuperscript 2 subscript 1 plus straight H presuperscript 2 subscript 1 rightwards arrow He presuperscript 3 subscript 2 plus straight n$
From the data given, we have
Total mass of reactant = $2 straight m left parenthesis straight H presuperscript 2 subscript 1 right parenthesis$
= 2(2.0141) amu
= (4.0282) amu
Total mass of product = $straight m left parenthesis He presuperscript 3 subscript 2 right parenthesis plus straight m subscript straight n$
= (3.0160) + (1.0087)
= 4.0247 amu
The decrease in mass is,
 $Δm space equals space left parenthesis 4.0282 minus 4.0247 right parenthesis amu$
= (0.0035) amu
= $5.8135 space cross times space 10 to the power of negative 30 end exponent kg$
The energy released during the reaction is,
 $space space straight E equals Δmc squared$
$equals 5.8135 space cross times space 10 to the power of negative 30 end exponent cross times left parenthesis 3 cross times 10 to the power of 8 right parenthesis squared$
$equals 5.23 cross times 10 to the power of negative 13 end exponent straight J$
$equals fraction numerator 5.23 cross times 10 to the power of negative 13 end exponent over denominator 1.6 cross times 10 to the power of negative 13 end exponent end fraction MeV$
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