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The following statement represents a nuclear reaction - Scottish Highers Physics - Question 14 - 2022

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The following statement represents a nuclear reaction. $^{238}_{94}Pu \rightarrow \;^{234}_{92}U + \;^{4}_{2}He$ The total mass of the particles before the reacti... show full transcript

Worked Solution & Example Answer:The following statement represents a nuclear reaction - Scottish Highers Physics - Question 14 - 2022

Step 1

Calculate the Mass Defect

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Answer

To find the mass defect, subtract the total mass after the reaction from the total mass before the reaction:

Δm=mbefore−mafter=(398.626×10−27kg)−(398.615×10−27kg)=0.011×10−27kg\Delta m = m_{before} - m_{after} = (398.626 \times 10^{-27} kg) - (398.615 \times 10^{-27} kg) = 0.011 \times 10^{-27} kg

Step 2

Convert Mass Defect to Energy Released

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Answer

Using Einstein's equation, E=Δmc2E = \Delta mc^2, where cc is the speed of light (c≈3×108 m/sc \approx 3 \times 10^8 \ m/s):

E=(0.011×10−27kg)(3×108 m/s)2E = (0.011 \times 10^{-27} kg) (3 \times 10^8 \ m/s)^2

Calculating this gives:

E=0.011×10−27kg×9×1016 m2/s2=9.9×10−12JE = 0.011 \times 10^{-27} kg \times 9 \times 10^{16} \ m^2/s^2 = 9.9 \times 10^{-12} J

Step 3

Select the Correct Answer

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Answer

The calculated energy released is approximately 9.9×10−139.9 \times 10^{-13} J, which corresponds to option D.

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