A gold nucleus has a radius of 7.3 ×10^-15 m and a charge of +79 e . Through what voltage must a

A gold nucleus has a radius of 7.3 ×10^-15 m and a charge of...

Key Concepts

Coulomb's Law

Coulomb's Law describes the force between two point charges, stating that the electrostatic force is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. It is fundamental when calculating the potential energy between charged particles and is widely used in problems involving nuclear interactions and particle accelerations.

Electric Potential Energy

Electric potential energy is the energy stored in a system of charges due to their positions. When two charges are separated by a distance, the work required to bring them from infinity to that separation is given by their electrostatic potential energy. This concept is key to determining the energy barriers that charged particles must overcome in order to interact or come within a specific distance of one another.

Acceleration of Charged Particles by Voltage

When a charged particle is accelerated through a voltage difference, it gains kinetic energy equal to the product of its charge and the voltage (qV). This principle is used to determine the amount of energy imparted to particles in accelerator physics and is crucial for understanding how particles can obtain sufficient energy to overcome electrostatic repulsion in collision experiments.

Conservation of Energy in Electrostatic Interactions

The conservation of energy principle ensures that the kinetic energy gained by a charged particle from being accelerated is converted into electrostatic potential energy as it approaches another charged object. This conversion is crucial for determining threshold conditions in problems where a particle must overcome a repulsive potential barrier. It ties together the energy imparted by accelerating a particle through a voltage and the energy required to reach a certain distance from another charge.

Transcript

00:01 Okay, so in this problem, we're told that we have a gold nucleus and a particle.

00:05 We want to get the particle near the gold nucleus.

00:08 So let's go ahead and write down some of the givens.

00:12 The radius of the gold nucleus is equal to 7 .3 times 10 to the minus 15 meters.

00:23 And the charge of gold is 79.

00:33 Times the charge of the electron.

00:36 And we want voltage needed for getting an alpha particle, a distance of 2 times 10 to the minus 14 meters from the surface of a gold nucleus.

00:57 So it's the, yeah.

01:00 So here's the gold nucleus.

01:02 And then here's our r -a -u, and then here's our...

01:11 Okay, so we want to use energy conservation.

01:15 So if there's no outside forces, which there are not, then the change in kinetic energy is equal to minus the change in potential energy because the, yeah, energy is conserved.

01:29 And so let's see.

01:33 So our goal is to get, so we know that the particle, actually, let me rewind.

01:48 So energy really isn't going to be conserved.

01:53 There is going to have to be some outside forest because it's not like an alpha particle will want to be near, oops, didn't mean to press that one, we'll want to be near the gold nucleus.

02:04 And so there is going to be a net external force.

02:07 So i'll start with the formula that i glossed over.

02:11 W net external is equal to change in you plus the change in kinetic energy.

02:18 So now let's simplify it a little.

02:20 So we're imagining starting the part of from rest and it's ending at rest because it's just barely made it.

02:25 So it's kinetic energy initially and finally are both zero.

02:32 So the net external force is going to be there's talking about.

02:39 So you're using a voltage to accelerate an alpha particle.

02:44 So, yeah, the work is going to generally be the force dotted with the distance.

02:51 So let's assume that these are parallel.

02:52 So we're dotting it, we're forcing it just in the proper direction that we're maximizing the increase in energy.

02:59 And then this l.

03:01 Force is going to be an electric force...

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