Consider an attractive nuclear force acting between two protons that can be expressed as F = Ce^ -kr /r^2 . Assume that k = 1 fermi^ -1 and the repulsive electric force between the protons is exactly balanced by the

Question

Quantrex Academy · Accepted Answer

Correct answer: D. 3.4 × 10^ -26 N m^2

The repulsive electric force between two protons is given by Coulomb's law:

F_{e} = \dfrac{1}{4\pi\epsilon_0} \dfrac{e^2}{r^2}

The attractive nuclear force is given by:

F_{n} = C \dfrac{e^{-kr}}{r^2}

At

r = 5 \text{ fermi}

, these forces balance each other, so

F_{e} = F_{n}

.

\dfrac{1}{4\pi\epsilon_0} \dfrac{e^2}{r^2} = C \dfrac{e^{-kr}}{r^2}

C = \dfrac{e^2}{4\pi\epsilon_0} e^{kr}

Given

k = 1 \text{ fermi}^{-1}

and

r = 5 \text{ fermi}

, we have

kr = 5

.

Substituting the known values:

\dfrac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ N m}^2/\text{C}^2

e = 1.6 \times 10^{-19} \text{ C}

e^5 \approx 148.4

C = (9 \times 10^9) \times (1.6 \times 10^{-19})^2 \times e^5

C = 9 \times 10^9 \times 2.56 \times 10^{-38} \times 148.4

C = 23.04 \times 10^{-29} \times 148.4

C \approx 3419 \times 10^{-29} \text{ N m}^2

C \approx 3.4 \times 10^{-26} \text{ N m}^2

Consider an attractive nuclear force acting between two protons...

Options

Correct answer

Step-by-step solution

More from Electric Field and Potential