Question

What is the total energy q released in a single fusion reaction event for the equation given in the problem introduction? use c2=1.49×10−10j/u?

Answer 1

`4.3\cdot 10^(-12) J`

Step-by-step explanation:

The fusion reaction in this problem is

`4^1_1H \rightarrow ^4_2He +2e^+`

The total energy released in the fusion reaction is given by

`\Delta E = c^2 \Delta m`

where

`c=3.0\cdot 10^8 m/s` is the speed of light

`\Delta m` is the mass defect, which is the mass difference between the mass of the reactants and the mass of the products

For this fusion reaction we have:

`m(^1_1H)=1.007825u` is the mass of one nucleus of hydrogen

`m(^4_2 He)=4.002603u` is the mass of one nucleus of helium

So the mass defect is:

`\Delta m =4m(^1_1 H)-m(^4_2 He)=4(1.007825u)-4.002603u=0.028697u`

The conversion factor between atomic mass units and kilograms is

`1u=1.66054\cdot 10^(-27)kg`

So the mass defect is

`\Delta m =(0.028697)(1.66054\cdot 10^(-27))=4.765\cdot 10^(-29)kg`

And so, the energy released is:

`\Delta E=(3.0\cdot 10^8)^2(4.765\cdot 10^(-29))=4.3\cdot 10^(-12) J`