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The following statement represents a nuclear fusion reaction - Scottish Highers Physics - Question 12 - 2023
Question 12
The following statement represents a nuclear fusion reaction. \( ^3_1H + ^3_1H \rightarrow ^4_2He + ^1_0n \) The total mass of the particles before the reaction is... show full transcript
Worked Solution & Example Answer:The following statement represents a nuclear fusion reaction - Scottish Highers Physics - Question 12 - 2023
Step 1
Calculate the mass defect
Answer
The mass defect is calculated by subtracting the total mass after the reaction from the total mass before the reaction:
[ \text{Mass defect} = \text{Mass before} - \text{Mass after} = (8.347 \times 10^{-17} - 8.317 \times 10^{-17}) \text{ kg} ]
[ \text{Mass defect} = 3.0 \times 10^{-20} \text{ kg} ]
Step 2
Convert mass defect to energy released
Answer
Using Einstein's mass-energy equivalence principle, the energy released can be calculated as follows:
[ E = mc^2 ] where:
- ( m ) is the mass defect
- ( c ) is the speed of light, approximately ( 3.00 \times 10^8 \text{ m/s} )
Substituting the values:
[ E = (3.0 \times 10^{-20} \text{ kg}) \times (3.00 \times 10^8 \text{ m/s})^2 ]
Calculating this gives:
[ E = 2.7 \times 10^{-12} \text{ J} ]
Step 3