Electrical Potential Energy Converted to Kinetic Energy

AI Thread Summary
The problem involves calculating the kinetic energy of an alpha particle released between two parallel plates with a potential difference of 330 V. The charge of the alpha particle is 3.20 x 10^-19 C, leading to an energy calculation of 1.056 x 10^-16 J when the voltage is multiplied by the charge. The distance between the plates does not factor into the kinetic energy calculation, as the energy is derived directly from the potential difference. Therefore, the kinetic energy of the alpha particle when it reaches the other plate is confirmed to be 1.056 x 10^-16 J. This demonstrates the conversion of electrical potential energy into kinetic energy without needing to consider distance.
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Homework Statement


The potential difference between two parallel conducting plates in vacuum is 330 V. An alpha particle with mass of 6.50 x10-27 kg and charge of 3.20 x10-19 C is released from rest near the positive plate. What is the kinetic energy of the alpha particle when it reaches the other plate? The distance between the plates is 34.0 cm.


Homework Equations


v = sqrt (2eV/m)
kinetic energy = electron volts?


The Attempt at a Solution


I tried to first calculate the electron volts: 330V (J/C) * 3.20E-19C = 1.056E-16 V
I know this electrical potential energy is converted into kinetic energy, but I'm not sure how to factor in the distance between the plates.
I know velocity equals the change in distance over the change in time, but I don't know the time, and can't solve with two unknowns.
I solved for velocity using the v = sqrt (2eV/m), and then plugged that and mass into the ke = 1/2 mv^2 equation, but got the same value as electron volts.
How do I factor in the distance?
Thanks!
 
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skibum143 said:

Homework Statement


The potential difference between two parallel conducting plates in vacuum is 330 V. An alpha particle with mass of 6.50 x10-27 kg and charge of 3.20 x10-19 C is released from rest near the positive plate. What is the kinetic energy of the alpha particle when it reaches the other plate? The distance between the plates is 34.0 cm.


Homework Equations


v = sqrt (2eV/m)
kinetic energy = electron volts?


The Attempt at a Solution


I tried to first calculate the electron volts: 330V (J/C) * 3.20E-19C = 1.056E-16 V



...


Note 330 volts = 330 joules per coulomb. If you multiply a potential difference (here 330 volts) by the charge of the alpha particle in coulombs the answer is an energy in joules, no more work need be done. The distance is not needed.
 
So joules is equal to kinetic energy, and 1.056E-16 J is the kinetic energy when it reaches the other plate?
 

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