Concept explainers
(a)
The radius of the
(a)
Answer to Problem 43P
The radius of the
Explanation of Solution
Write the expression for the radius of the
Here,
Conclusion:
Substitute
Therefore, the radius of the
(b)
The force of repulsion between a proton at the surface of an
(b)
Answer to Problem 43P
The force of repulsion between a proton at the surface of an
Explanation of Solution
Write the expression for the force of repulsion between a proton at the surface of an
Here,
Conclusion:
Substitute
Therefore, the force of repulsion between a proton at the surface of an
(c)
The work done to overcome the last proton from a large distance up to the surface of the nucleus.
(c)
Answer to Problem 43P
The work done to overcome the last proton from a large distance up to the surface of the nucleus is
Explanation of Solution
Write the expression for the work done to overcome the last proton from a large distance up to the surface of the nucleus.
Conclusion:
Substitute
Therefore, the work done to overcome the last proton from a large distance up to the surface of the nucleus is
(d)
The radius of
(d)
Answer to Problem 43P
The radius of
Explanation of Solution
Use equation (I) to solve for the radius of
Use equation (II) to solve for force between a proton at the surface of
Use equation (III) the work done to overcome the last proton from a large distance up to the surface of the nucleus.
Conclusion:
Substitute
Substitute
Substitute
Therefore, the radius of
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Chapter 30 Solutions
Principles of Physics: A Calculus-Based Text
- (a) Show that if you assume the average nucleus is spherical with a radius r=r0A1/3, and with a mass at A u, then its density is independent at A. (b) Calculate that density in u/fm3 and kg/m3, and compare your results with those found in Example 31.1 for 56Fe.arrow_forwardIf two nuclei are to fuse in a nuclear reaction, they must be moving fast enough so that the repulsive Coulomb force between them does not prevent them for getting within R1014mof one another. At this distance or nearer, the attractive nuclear force can overcome the Coulomb force, and the nuclei are able to fuse. (a) Find a simple formula that can be used to estimate the minimum kinetic energy the nuclei must have if they are to fuse. To keep the calculation simple, assume the two nuclei are identical and moving toward one another with the same speed v. (b) Use this minimum kinetic energy to estimate the minimum temperature a gas of the nuclei must have before a significant number of them will undergo fusion. Calculate this minimum temperature first for hydrogen and then for helium. (Hint: For fusion to occur, the minimum kinetic energy when the nuclei are far apart must be equal to the Coulomb potential energy when they are a distance R apart.)arrow_forward(a) Calculate the number of grams of deuterium in an 80.000L swimming pool, given deuterium is 0.0150% of natural hydrogen. (b) Find the energy released in joules if this deuterium is fused via the reaction 2H+2H3He+n. (c) Could the neutrons be used to create more energy? (d) Discuss the amount of this type of energy in a swimming pool as compared to that in, say, a gallon of gasoline, also taking into consideration that water is far more abundant.arrow_forward
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