What Voltage Is Required to Double an Alpha Particle's Velocity?

[vitaly]

An alpha particle is accelerated to a velocity v in a particle accelerator by a potential difference of 1200 V. Which of the following potential differences would be needed to give the alpha particle twice the velocity?

A. 7200 V
B. 4800 V
C. 4100 V
D. 2400 V
E. 1700 V

At first, I thought of a ratio. That means doubling the speed would double the voltage. But, the answer that I thought of, 2400 V, seems too obvious... Is there any certain equation I can use to be certain of my answer? All help is appreciated.

 

[dextercioby]

Nope.4 times more...Do you see why?HINT:Think where does the KE of the particle (nonrelativistic,for simplicity) comes from...

Daniel.

 

[thepatientmental]

To find the potential difference needed to give the alpha particle twice the velocity, we can use the equation for kinetic energy: KE = 1/2 mv^2, where m is the mass of the alpha particle and v is its velocity. Since we want to double the velocity, we can set up the equation as follows:

KE1 = 1/2 mv^2

KE2 = 1/2 m(2v)^2

Since the mass of the alpha particle remains the same, we can cancel it out from both equations. This leaves us with:

1/2 v^2 = 1/2 (2v)^2

Simplifying, we get:

1/2 v^2 = 1/2 4v^2

1/2 v^2 = 2v^2

v^2 = 4v^2

v^2 - 4v^2 = 0

-3v^2 = 0

v = 0

This means that the potential difference needed to give the alpha particle twice the velocity would be 2400 V. Therefore, the correct answer is D. 2400 V. This may seem too obvious, but it is the correct answer based on the given information and the equation for kinetic energy.