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The following statement describes a fusion reaction - Scottish Highers Physics - Question 12 - 2015
Question 12
The following statement describes a fusion reaction. \( {}^1H + {}^1H \rightarrow {}^4He + {}^1n + \text{energy} \) The total mass of the particles before the reac... show full transcript
Worked Solution & Example Answer:The following statement describes a fusion reaction - Scottish Highers Physics - Question 12 - 2015
Step 1
Calculate the mass defect
Answer
To find the energy released, we first need to calculate the mass defect, which is the difference between the total mass before and after the reaction. The mass defect ( \Delta m ) can be calculated as follows:
[ \Delta m = \text{mass before} - \text{mass after} = (6.684 \times 10^{-27} \text{ kg}) - (6.680 \times 10^{-27} \text{ kg}) = 4.00 \times 10^{-30} \text{ kg} ]
Step 2
Convert the mass defect to energy
Answer
Using Einstein's mass-energy equivalence principle, we can convert the mass defect into energy using the formula:
[ E = \Delta m c^2 ]
where ( c ) is the speed of light in vacuum (approximately ( 3.00 \times 10^8 \text{ m/s} )). Thus,
[ E = (4.00 \times 10^{-30} \text{ kg}) \times (3.00 \times 10^8 \text{ m/s})^2 ]
This results in:
[ E \approx 3.600 \times 10^{13} \text{ J} ]
Step 3