Chapter 32, Problem 41PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
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,

â€ƒâ€ƒr=r0A1/3â€ƒâ€ƒ.........(1)

Here, r0 is a constant of the nucleus which has a value 1.2Ã—10âˆ’15m.

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

â€ƒâ€ƒEk=32kBTâ€ƒâ€ƒ.........(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,

â€ƒâ€ƒEp=kq2dâ€ƒâ€ƒ.........(3)

Here, k is the Coulomb constant.

Calculation:

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

â€ƒâ€ƒr=r0A1/3=1.2Ã— 10 âˆ’15m31/3=1.7307Ã—10âˆ’15m

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,

â€ƒâ€ƒd=2r=2Ã—1.7307Ã—10âˆ’15m=3.4614Ã—10âˆ’15m

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

â€ƒâ€ƒEp=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.

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