Respuesta :
Given:
The distance between electron and proton is
[tex]r=6.4\times10^{-11}\text{ m}[/tex]Required:
The Coulomb's force and gravitational force.
Explanation:
The Coulomb's force between electron and proton can be calculated by the formula
[tex]F_c=k\frac{|q_eq_p|}{r^2}[/tex]Here, k is the constant whose value is
[tex]k\text{ = 9}\times10^9\text{ N m}^2\text{ /C}^2[/tex]The charge of an electron is
[tex]q_{_e}=-1.6\times10^{-19\text{ }}C[/tex]The charge of the proton is
[tex]q_p=\text{ 1.6}\times10^{-19}\text{ C}[/tex]On substituting the values, Coulomb's force will be
[tex]\begin{gathered} F_c=\frac{9\times10^9\times1.6\times10^{-19}\times1.6\times10^{-19}}{(6.4\times10^{-11})^2} \\ =5.625\times10^{-8}\text{ N} \end{gathered}[/tex]The gravitational force can be calculated by the formula
[tex]F_g=\frac{Gm_em_p}{r^2}[/tex]Here, G is the universal gravitational constant whose value is
[tex]G\text{ = 6.67}\times10^{-11}\text{ N m}^2\text{ /kg}^2[/tex]The mass of the electron is
[tex]m_e=9.1\times10^{-31}\text{ kg}[/tex]The mass of the proton is
[tex]m_p=1.67\times10^{-27}\text{ kg}[/tex]On substituting the values, the gravitational force will be
[tex]\begin{gathered} F_g=\frac{6.67\times10^{-11}\times9.1\times10^{-31}\times1.67\times10^{-27}}{(6.4\times10^{-11})^2} \\ =2.47\times10^{-47}\text{ N} \end{gathered}[/tex]Final Answer: Coulomb's force is 5.625e-8 N
Gravitational force is 2.47e-47 N
