0

$$H_1^2 + H_1^2 \rightarrow He^4_2+ \text{energy}$$

How can energy be released, if the left hand side of this equation has less mass/energy than the right?

$\text{BE}_H \approx 1 \text{MeV}\\ \text{BE}_{He} \approx 11 \text{MeV}$

BE = binding energy per nucleon

The energy equation would therefore be

$$ 2\cdot 2 \cdot (1\text{MeV}) \rightarrow 4\cdot (11\text{MeV}) + n$$

Making $n$ negative.

I know this fusion is usually done with $H_1^3$ (Tritirium?), does this make a difference?

With this, a proton would be emitted, would that be the energy from equation 1?

Tobi
  • 1,819
  • 3
  • 16
  • 29

1 Answers1

2

I think you got the fusion reaction slightly wrong, what is happening in the end is

\begin{eqnarray} ^{2}\mbox{H} +\ ^{2}\mbox{H} &\rightarrow& ^{3}\mbox{H} +\ ^{1}\mbox{H}\\ ^{2}\mbox{H} +\ ^{2}\mbox{H} &\rightarrow& ^{3}\mbox{He} + \mbox{n}, \end{eqnarray}

which both have approximately the same probability to occur. Note that the released kinetic energy is not included in the reactions above.

Insert the atomic masses results in

\begin{eqnarray} 2.01410177812\cdot u + 2.01410177812\cdot u &=& 3.0160492779\cdot u + 1.00782503223\cdot u + x_1\\ 2.01410177812\cdot u + 2.01410177812\cdot u &=& 3.0160293201 \cdot u + 1.00866491588\cdot u + x_2 \end{eqnarray}

where $x_{1,2}$ corresponds to the released energy. The data for the atomic masses is from the NIST website and from wikipedia.

Solving the equatione yields

\begin{eqnarray} x_1 &\approx& 0.00432924611\cdot u\\ x_2 &\approx& 0.00350932026\cdot u \end{eqnarray}

corresponding to ($1\cdot u$ corresponds approximately to $931.5$ MeV)

\begin{eqnarray} x_1 &\approx& 4.03\,\mathrm{MeV}\\ x_2 &\approx& 3.27\,\mathrm{MeV}. \end{eqnarray}

So this is the released energy for both reactions, does the reaction ''equation'' now makes more sense to you?

Alf
  • 2,039