A plutonium- 239 nucleus initially at rest undergoes alpha decay to produce a uranium-235 nucleus. The uranium-235 nucleus has a mass of 3.90 x 10^-25 kg and moves away with a speed of 2.62 x 10^5 m/s. Determine the minimum wage electric potential difference that is required to bring the alpha particles to rest. This question is worth 12 marks and marks are awarded based in the two physics principles u choose from below and your final answer.
uniform motion
accelerated motion
circular motion
work energy 5heorem
conservation of momentum
conservation of mass energy
conservation of charge
cpnserbation of nucleons
wave particle duality
I wanted to find the velocity of the alpha particle through conservation of momentum and the. Ek= vq. I dont understand how this could possibly,y be worth 12 marks but also how this uses two physics COncepts! I would really appreciate some feedback on where I went wrong.
To find the minimum wage electric potential difference required to bring the alpha particles to rest, you can use the principle of conservation of momentum and the work-energy theorem.
First, let's determine the initial momentum of the plutonium-239 nucleus. Since it is initially at rest, its momentum is zero.
Next, let's determine the final velocity of the uranium-235 nucleus by using conservation of momentum. Since the alpha particle decays into a uranium-235 nucleus, the momentum before and after the alpha decay should be equal.
Conservation of momentum equation:
Initial momentum = Final momentum
Since the plutonium-239 nucleus is at rest, its initial momentum is zero. Therefore, the final momentum is also zero.
Final momentum can be calculated as the product of the mass and velocity of the uranium-235 nucleus:
Final momentum = mass x velocity
Plugging in the values:
0 = (3.90 x 10^-25 kg) x (2.62 x 10^5 m/s)
Now, solve for the minimum wage electric potential difference required to bring the alpha particles to rest using the work-energy theorem.
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
The equation for work is:
Work = Change in kinetic energy
The work done to bring the alpha particles to rest can be calculated as the charge of the alpha particles multiplied by the electric potential difference (voltage). The voltage is what we need to determine.
Work = Charge x Voltage
Since the alpha particles lose all their kinetic energy and come to rest, the work done on them is equal to their initial kinetic energy (Ek = 0.5mv^2), which is also the change in kinetic energy.
Plugging in the values:
0 = (0.5) x (3.90 x 10^-25 kg) x (2.62 x 10^5 m/s)^2 x Voltage
Now, solve for the voltage:
Voltage = 0 / [(0.5) x (3.90 x 10^-25 kg) x (2.62 x 10^5 m/s)^2]
After simplifying the equation, you should find that the voltage required is zero. This means no external electric potential difference is necessary to bring the alpha particles to rest after alpha decay.
It seems that you have mentioned only using the principle of conservation of momentum in your explanation. However, by also using the work-energy theorem, you have employed two concepts: conservation of momentum and work-energy theorem.
Regarding the marks, it is up to the teacher or the exam board to allocate marks based on the complexity of the question and the correct application of physics principles.