   Chapter 32, Problem 41PE

Chapter
Section
Textbook Problem

Integrated Concepts:(a) What temperature gas would have atoms moving fast enough to bring two 3He nuclei into contact? Note that, because both are moving, the average kinetic energy only needs to be half the electric potential energy of these doubly charged nuclei when just in contact with one another.(b) Does this high temperature imply practical difficulties for doing this in controlled fusion?

To determine

(a)

The temperature of the gas that would have atoms moving fast enough to bring two H3e nuclei into contact.

Explanation

Given:

Mass number of H3eA=3

Nuclear charge on H3eq=2e , where e is the electronic charge.

Formula used:

The nuclear radius r of a nucleus is given by,

r=r0A1/3  .........(1)

Here, r0 is a constant of the nucleus which has a value 1.2×1015m.

The kinetic energy Ek of the nucleus is related to the temperature T of the gas as follows:

Ek=32kBT  .........(2)

Here, kB is the Boltzmann's constant.

The potential energy of two nuclei each of charge q at a distance d from each other is given by,

Ep=kq2d  .........(3)

Here, k is the Coulomb constant.

Calculation:

Calculate the radius of the H3e nucleus using equation (1).

r=r0A1/3=1.2× 10 15m31/3=1.7307×1015m

When the two H3e come in contact with each other, the distance between their centers is d which is equal to twice the radius of each nucleus.

Therefore,

d=2r=2×1.7307×1015m=3.4614×1015m

Using equation (3) write an expression for the potential energy of the system.

Ep=kq2d=k 2e 2d

When the two H3e move towards each other, the total kinetic energy of two H3e nuclei is equal to the electrostatic potential energy of the system

To determine

(b)

If the high temperature calculated in (a) poses practical difficulties in controlled fusion.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 