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Read the following passage and answer the accompanying questions - Leaving Cert Physics - Question 10 - 2007
Question 10
Read the following passage and answer the accompanying questions. Ernest Walton was one of the legendary pioneers who made 1932 the annus mirabilis of experimental ... show full transcript
Worked Solution & Example Answer:Read the following passage and answer the accompanying questions - Leaving Cert Physics - Question 10 - 2007
Step 1
Draw a labelled diagram to show how Cockcroft and Walton accelerated the protons.
Answer
The diagram should include:
- A labeled anode and cathode.
- A depiction of a proton being accelerated by a high potential difference (PD).
- Indicate the lithium target where the two helium nuclei are produced.
Show the relationship:
[ PD = \frac{W}{H} ]
Step 2
What is the velocity of a proton when it is accelerated from rest through a potential difference of 700 kV?
Answer
Using the work-energy principle:
[ W = q \cdot V ]
Where:
- ( q = 1.6022 \times 10^{-19} , C ) (charge of proton)
- ( V = 700 \times 10^{3} , V )
Calculate the kinetic energy:
[ W = (1.6022 \times 10^{-19}) \cdot (700 \times 10^{3}) = 1.12154 \times 10^{-10} , J ]
Using ( KE = \frac{1}{2}mv^2 ):
[ v = \sqrt{\frac{2W}{m}} = \sqrt{\frac{2 \times 1.12154 \times 10^{-10}}{1.676 \times 10^{-27}}} ]
Calculating: [ v \approx 1.16 \times 10^{7} , m/s ]
Step 3
Step 4
Calculate the energy released in this disintegration.
Answer
Calculating using the masses:
- Mass of reactants = ( 1.1646 \times 10^{-26} + 1.6726 \times 10^{-27} = 1.33186 \times 10^{-26} , kg )
- Mass of products = ( 2.6643 \times 10^{-27} \times 2 = 5.3286 \times 10^{-27} , kg )
Using ( E = mc^2 ):
[ E = (3.00 \times 10^{8} \text{ m/s})^2 \times (\text{mass difference}) ]
[ E = (3.00 \times 10^{8})^2 \times (1.33186 \times 10^{-26} - 5.3286 \times 10^{-27}) ]
Calculating the energy released in the disintegration.