The Physical Universe
The Physical Universe
15th Edition
ISBN: 9780073513928
Author: Konrad Krauskopf, Arthur Beiser
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 8, Problem 58E
To determine

Check whether the gravitational force between two protons in nucleus is balanced by their electrical repulsion, calculate the ratio of this electrical force to the gravitational force and determine whether this ratio has any dependence on the distance between the protons.

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Answer to Problem 58E

No. The value of Fele/Fg is 1.24×1036 and is independent of the distance between protons.

Explanation of Solution

The gravitational force between two protons in a nucleus is too weak in comparison with the electoral repulsive force between them. In femtometer (1fm=1015m) range, strong nuclear force is the dominant attractive force.

Write the formula to calculate the magnitude of Columb electrical force between two protons.

Fele=14πε0e2r2 (1)

Here,

Fele is the Columb electric force between protons

ε0 is the permittivity of free space

e is the magnitude charge of electron

r is the distance of separation between protons

Write the formula to calculate the magnitude of gravitational force between two protons.

Fg=Gmp2r2 (2)

Here,

Fg is the gravitational force between the protons

G is the gravitational constant

mp is the mass of proton

Divide equation (1) by equation (2).

FeleFg=(14πε0e2r2)(Gmp2r2)=14πε0e2Gmp2

Substitute 9×109Nm2/C2 for 1/4πε0,1.6×1019C for e,6.67×1011Nm2/kg2 for G and 1.67×1027kg for mp in the above equation to find FeleFg.

FeleFg=(9×109Nm2/C2)(1.6×1019C)2(6.67×1011Nm2/kg2)(1.67×1027kg)2=1.24×1036

The above ratio shows that Fele is 1.24×1036 times stronger than Fg. This means that Fele cannot be counteracted by Fg. The relation FeleFg=14πε0e2Gmp2 is independent of term r. This means that separation between protons has no any role determining the value of FeleFg.

Conclusion: Therefore, force of gravity between protons is not balanced by their electrical repulsive force, the value of Fele/Fg is 1.24×1036 and is independent of the distance between protons.

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Chapter 8 Solutions

The Physical Universe

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