The probability of a nuclear reaction increases dramatically...

Name: Problem 14, Chapter 45: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2020-06-01T08:44:15-08:00
Duration: 5 min 4 s
Channel: Ren Jie Tuieng
Description: The probability of a nuclear reaction increases dramatically when the incident particle is given energy above the "Coulomb barrier," which is the electric potential energy of the two nuclei when their surfaces barely touch. Compute the Coulomb barrier for the absorption of an alpha particle by a gold nucleus.

The probability of a nuclear reaction increases dramatically when the incident particle is given energy above the "Coulomb barrier," which is the electric potential energy of the two nuclei when their surfaces barely touch. Compute the Coulomb barrier for the absorption of an alpha particle by a gold nucleus.

Key Concepts

Electric Potential Energy

This concept involves the energy stored due to the positions of charges, described by Coulomb’s law. In nuclear physics, the electric potential energy between two nuclei is calculated at the distance where their surfaces nearly touch and determines the height of the Coulomb barrier.

Nuclear Radius and Scaling Law

In estimating the separation at which two nuclei interact, the nuclear radius plays a crucial role. The radius is typically approximated by the formula R = r?A^(1/3), where r? is a constant and A is the mass number. This scaling law is essential for determining the distance between the incident particle and the target nucleus at the point of contact.

Coulomb Barrier

The Coulomb barrier refers to the electrostatic energy barrier due to the repulsive interaction between two positively charged nuclei. It represents the minimum kinetic energy that an incident charged particle must possess to overcome this repulsion and get close enough for the attractive strong nuclear force to initiate a nuclear reaction.

Charged Particle Interactions in Nuclear Reactions

This concept highlights the behavior of charged particles, such as alpha particles, during nuclear reactions. Their interactions are dominated by the competing effects of electrostatic repulsion and the attractive nuclear force, with the Coulomb barrier being the critical threshold that must be overcome for a reaction to occur.

Transcript

00:01 We'll give it the definition of the coulome barrier as the electric potential energy, epe, when two of the nuclei, the touch, right, barely touch on the surface.

00:18 So we want to find why is the coulum barrier for absorption of an alpha particle by a gold nucleus.

00:25 So we assume the left side is the alpha particle, right, is the gold nucleus.

00:30 I want to find the coulomb barrier, which is basically.

00:32 The electric potential energy.

00:36 So to calculate the electric potential energy, we actually need the distance because electric potential energy is actually given as your charge of your the multiplication of the charges between the two nuclei by 4 pi epsilon not times r, where r is your distance between between the centers of the two nuclei.

01:14 And the r is actually given as your r of your alpha, which is radius of our alpha nucleus, and the radius plus the radius of the gold nucleus, right, when these two nuclei are barely touching.

01:33 So in order to get what is the radius of the alpha particle and the gold nuclei, we can use the approximation that's r is equals to r not which is a constant 1 .2 fermis multiplied by the nucleon number to the power of one third this is an approximation from using fitting methods of the experimental from experimental data that we get this formula and so we know for alpha particle, the a value, which is the nucleon number is 4.

02:28 For the gold nuclei, we'll have to look up the nucleon number for gold.

02:41 And for gold, the nucleon number is 197.

02:52 So there will be anode times 197 to the power of...

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