Potential energy( electron moving away form proton)

[whynot314]

An electron is initially 2cm from a proton and is then give an initial velocity away from the proton. If v is 31m/s how far to the right does the electron move before it momentarily stops?

is this right?
[PLAIN]http://i1341.photobucket.com/albums/o745/nebula-314/IMAG0112_zps5361921d.jpg[/PLAIN]

 

[Simon Bridge]

You should state your reasoning... it looks like you are saying that the initial kinetic energy of the electron goes to change it's the potential energy.

The way to gain confidence in your answer is to see if it makes sense.
So you need something to compare the distance with.

 

[whynot314]

well I am not really sure as to what to compare it to because I am given a specific initial velocity.

 

[Simon Bridge]

Is that a fast speed do you think?
i.e.
is the speed relativistic?
is this electron bound to the proton?
can you look up what sort of speeds to expect for electrons to get a feel for how far they may move from protons?

One of the most important parts of learning physics is developing a feel for the way things work.

FWIW: your reasoning is sound - conservation of energy is a solid argument.
Short of double-checking your arithmetic (did you use the right numbers? did you keep track of the minus signs?) and making sure there are no energy losses you've forgotten about - you should be fine.

I just think you should start getting used to looking at your answers and asking if they make sense ... the distance moved here is almost 1mm ... this is very big compared to an atom but the electron starts out 2cm away from the proton so it does not look like it should be bound - so you should expect a large displacement to be possible. You could also work out what the speed would be when the electron is close to the proton (r=0).

 

[Nickie]

Yes, your calculation appears to be correct. The electron will move to the right for a certain distance before momentarily stopping due to the decrease in potential energy as it moves away from the proton. This distance can be calculated using the equation for potential energy, where the initial potential energy (U1) is equal to the final potential energy (U2) plus the kinetic energy (K):

U1 = U2 + K

Since the electron starts with an initial potential energy of zero (since it is 2cm from the proton), we can rearrange the equation to solve for the distance the electron will move (x):

x = (K/U2) * 2cm

Plugging in the given values, we get:

x = (0.5 * m * v^2)/(2 * k * q1 * q2 / r)

= (0.5 * 9.11 x 10^-31 kg * (31 m/s)^2) / (2 * 8.99 x 10^9 Nm^2/C^2 * 1.6 x 10^-19 C * 1.6 x 10^-19 C / 2cm)

= 5.06 x 10^-10 m = 0.506 nm

So the electron will move to the right for 0.506 nanometers before momentarily stopping. This calculation assumes that the proton remains stationary, as it is significantly more massive than the electron and will not move significantly due to the electron's motion.