Question

You are planning a set of experiments to study the forces between nuclei by shooting alpha particles from a Van de Graaf accelerator at a sheet of lead. The alpha particle is the nucleus of a helium atom (2 protons, 2 neutrons). The lead nucleus contains 82 protons, 125 neutrons. Mass of the neutron is almost the same as the proton. The alpha particle should come into contact with a lead nucleus. Assume both particle and nucleus are the shape of a sphere. Alpha particle has a radius of 10x10^-13 cm and the lead radius is 4 times larger. Find minimum speed of alpha particle w/ lead at rest

Answer 1

The coulomb force falls off pretty quickly (r^-2), and we can use this fact to find a good approximation for this problem.

Of course, the minimum speed needed will be when the two spheres strike one another head on. This will ensure that all the kinetic energy will be directed straight into the lead nucleus.

So, if we were to take an alpha particle from an infinite distance away, and push it until it's 10*10^-13cm away, how much energy would this take? Another way to ask this is: if an alpha particle were 10*10^-13 cm away from the center of a nucleus, what would be the electrical potential energy?

Answer 2

Hmm. I'm still new to the electrical potential energy thing... would it have potential energy or just kinetic?

Answer 3

Well, right now we're just looking at the potential energy of a very specific arrangement of charges.

An alpha particle has a charge of 2. A lead nucleus has a charge of 82. What would be the electrical potential energy of an alpha particle sitting 10*10^-13cm away from the lead nucleus? Do you know the equation to find this?

Answer 4

is it the k(q1)(q2)/r equation?

Answer 5

1.5 x 10^26 joules?

Answer 6

Yep.

Now, that value is the amount of energy that is needed to bring the alpha particle in to the nucleus from a large distance. Said exactly, it's the energy needed to bring the particle in from an infinite distance. However, the coulomb force falls off pretty quickly, so we can approximate the starting distance of the particle to be "inifinity."

So, that number now is the energy needed to put the alpha particle within the radius of the nucleus.

Can you see the next step?

Answer 7

set that number equal to 1/2mv^2 to solve for velocity?

Answer 8

There ya go :)

Answer 9

sweet!! thanks man, I think i can see it from here. thanks for the patience!

Answer 10

My pleasure :)

Answer 11

@Vandreigan


isn't it this?