Elastic collision of an alpha particla and Lead

[panders3]

Homework Statement

An a particle of mass 6.6 x 10-27 kg came closest to an atom of lead with a distance of 4.8 x 10-14 m. At what velocity will the a particle rebound directly away if the collision is totally elastic?

Mass of the Alpha Particle - 6.6 x 10^-27 kg
Alpha particles are 2n2p

Mass of Lead Particle - 3.44 x 10^-25kg


Distance between the two particles when the elastic collision occurs - 4.8 x 10^-14 m

Homework Equations

v = f$$\lambda$$
Ek = hf – W

The Attempt at a Solution

I am not sure how to find the energy at which the elastic collision will occur. I assume it has to do with the atomic number of lead and the alpha particle, but i cannot find the theory behind it in my text.

 

[gneill]

Consider the potential energy due to the electric field that exists between the lead nucleus and the alpha particle at the instant of their minimum separation.

 

[panders3]

so then to find the electric field you use E= (kq1q2)/r where q1 would be the charge on the lead and q2 would be the charge on the alpha particle r would be the minimum distance. Then e would be the potential energy which would then be converted to kinetic energy as the alpha particle moves away.

I would need to assume that because the lead stays still?

 

[gneill]

Conveniently, the author of the problem did not specify a frame of reference to use. So if you were to consider the instant when the lead atom and the alpha particle are at their minimum distance (and at rest with respect to each other at that instant) and take the center of mass at that moment as the origin of your frame of reference, you may find your life much easier!

 

[rwisz]

As a scientist, it is important to have a strong understanding of the principles and equations involved in a problem before attempting to solve it. In this case, the elastic collision between an alpha particle and lead can be analyzed using the principles of conservation of momentum and conservation of energy.

First, we can calculate the initial velocity of the alpha particle using the given mass and distance. Using the equation v = fλ, we can rearrange it to solve for velocity (v = λf). In this case, the frequency (f) can be calculated using the speed of light (c) and the given wavelength (λ), which is the distance between the two particles during the collision. This will give us the initial velocity of the alpha particle before the collision.

Next, we can use the principle of conservation of momentum to calculate the final velocity of the alpha particle after the collision. Since the collision is elastic, we know that the total momentum before and after the collision must be equal. This means that the final velocity of the alpha particle can be calculated by setting the initial momentum equal to the final momentum (mv = mv).

Finally, we can use the principle of conservation of energy to determine the energy at which the elastic collision will occur. This can be calculated using the equation Ek = hf - W, where Ek is the kinetic energy, h is Planck's constant, f is the frequency, and W is the work done during the collision. The work done can be calculated using the initial and final velocities of the alpha particle, as well as the mass of the lead particle.

By solving for the final velocity and energy, we can determine the velocity at which the alpha particle will rebound directly away from the lead atom after the elastic collision. It is important to note that this calculation assumes a perfectly elastic collision, meaning that there is no loss of energy during the collision. In reality, there may be some loss of energy due to factors such as friction or deformation of the particles. However, this calculation provides a theoretical estimate of the final velocity and energy in an ideal scenario.