Finding the potential difference of an alpha particle.

[elephantorz]

1. Through what potential difference ($$\Delta$$V) would you need to accelerate an alpha particle, starting from rest, so that it will just reach the surface of a 15 x 10^(-15) m $$^{238}$$U nucleus?
2. KE = q$$\Delta$$V
E = $$\gamma_{p}$$mc²
r = $$\frac{mv}{qB}$$
3. Ok, I feel like I am close to what I really need but I am lacking something...
You can get the charge (q) and mass for both the particle and the U nucleus from the information given, you can also get the radius of the nucleus if needed.

I have that, I just seem to have two unknowns for every equation I am using, if I solve for u in E = $$\gamma_{p}$$mc² I don't know Energy, and if I solve for v or B in
r = $$\frac{mv}{qB}$$ I don't know one of them, what am I missing?

 

[Shooting Star]

Where did the B come from?

If the alpha particle just reaches the surface of the nucleus, its KE is zero, but PE is not.

But how much KE it should have had to reach that point? Remember conservation of energy.

Knowing the charge of the alpha particle, what should be ∆V to give that KE at a point far away from the nucleus?

There, I just solved it for you.

 

[Moetasim]

I would like to clarify that the potential difference is not the only factor that determines the motion of an alpha particle. Other factors such as the magnetic field, electric field, and particle's initial velocity also play a role.

To find the potential difference needed to accelerate an alpha particle to reach the surface of a 15 x 10^(-15) m ^{238}U nucleus, we can use the formula for kinetic energy (KE) which is equal to the product of charge (q) and potential difference (\DeltaV). We also know that the kinetic energy is equal to the relativistic energy (E) of the particle, which can be calculated using the formula E = \gamma_{p}mc², where \gamma_{p} is the Lorentz factor, m is the mass of the particle, and c is the speed of light.

To find the velocity of the alpha particle, we can use the formula r = \frac{mv}{qB}, where r is the radius of the circular motion, m is the mass of the particle, v is the velocity, q is the charge, and B is the magnetic field. We can rearrange this formula to solve for v, which will give us the velocity of the particle.

In order to solve for the potential difference, we need to know the velocity of the alpha particle, which we can calculate using the above formula. We also need to know the charge and mass of the alpha particle, which can be obtained from the given information. Additionally, we need to know the magnetic field, which can be calculated using the radius of the nucleus and the velocity of the particle.

Therefore, to find the potential difference, we need to use all the given information and equations to solve for all the unknowns. It is possible that we may need to use multiple equations and rearrange them to solve for the potential difference. I suggest reviewing the equations and making sure all the given information is used correctly to find the potential difference.