Respuesta :
To solve this problem, we make use of the Coulumb’s law which relates the electrical force to the charges. The formula used in Coulumb’s law is given as:
F = k q1 q2 / r^2
where,
F = electric force = 2.3 * 10^-26 N
k = Coulumb’s constant = 9 * 10^9 N m^2/C^2
q1 = q2 = electric charge of protons = 1.602 * 10^-19 C
r = distance between the two protons
Substituting the given values:
2.3 * 10^-26 N = (9 * 10^9 N m^2/C^2) (1.602 * 10^-19 C)^2 / r^2
r^2 = 0.01 m^2
r = 0.1 m
Therefore the protons are only 0.1 m apart or 10 cm.
The magnitude of the force between two protons depends on the charge of protons and the distance between them which is stated in the coulomb's law. The distance between two protons is 0.1 m.
What is Coulomb's law?
The coulomb's law states that the magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.
Given that the magnitude of electric force F between two protons is 2.3 X 10^{-26} N. We know that the charge at the proton is 1.602 X 10^-19 C.
The force between two protons with a distance of d apart is given as below.
[tex]F = \dfrac {kq_1q_2}{d^2}[/tex]
Where k is Coulomb's constant which is 9 X 10^9 N m^2/C^2 and q1 and q2 are electric charges of protons.
[tex]2.3 \times 10^{-26} = \dfrac {9\times 10^9 \times 1.602 \times 10^{-19} \times 1.602 \times 10^{-19}}{d^2}[/tex]
[tex]d^2= \dfrac {9\times 10^9 \times 1.602 \times 10^{-19} \times 1.602 \times 10^{-19}}{2.3 \times 10^{-26} }[/tex]
[tex]d^2 = 0.01[/tex]
[tex]d = 0.1 \;\rm m[/tex]
Hence we can conclude that the protons are 0.1 m apart.
To know more about the coulomb's law, follow the link given below.
https://brainly.com/question/26115859.
