Respuesta :
Answer:
The ratio of the greater force to the lesser force is:
Explanation:The masses of protons and electron, and the distance between them are given below.
[tex]\begin{gathered} m_p=1.67\times10^{-11}kg \\ \\ m_e=9.11\times10^{-31}kg \\ \\ r=4.67\times10^{-11}kg \\ \\ G=6.67\times10^{-11}m^3kg^{-1}s^{-2} \end{gathered}[/tex]The gravitational force between the proton and electron is calculated below
[tex]\begin{gathered} F_g=\frac{Gm_1m_2}{r^2} \\ \\ F_g=\frac{6.67\times10^{-11}\times1.67\times10^{-27}\times9.11\times10^{-31}}{(4.67\times10^{-11})^2} \\ \\ F_g=4.65\times10^{-47}N \end{gathered}[/tex]The magnitude of the charge on a proton and an electron is the same, and is given as:
[tex]\begin{gathered} q_p=1.6\times10^{-19}C \\ \\ q_e=1.6\times10^{-19}C \end{gathered}[/tex]The electrostatic force between the proton and electron is then calculated as:
[tex]\begin{gathered} F_E=\frac{kq_pq_e}{r^2} \\ \\ F_E=\frac{9\times10^9\times1.6\times10^{-19}\times1.6\times10^{-19}}{(4.67\times10^{-11})^2} \\ \\ F_E=1.056\times10^{-7}N \end{gathered}[/tex]As seen above, the electrostatic force is the greater force, while the gravitational force is the lesser force
The ratio of the greater to the lesser force is:
[tex]\begin{gathered} \frac{F_E}{F_g}=\frac{1.056\times10^{-7}}{4.65\times10^{-47}} \\ \\ \frac{F_E}{F_g}=2.27\times10^{39} \end{gathered}[/tex]