Question

A hydrogen atom contains a proton, mass 1.67 x 10-27 kilograms, and an electron, mass 9.11 x 10-31 kilograms. The average distance between them is 4.67 x 10-11 meters. The proton and the electron exert both a gravitational force and an electrostatic force on each other.What is the ratio of the greater force to the lesser force?

Answer 1

Answer:

The ratio of the greater force to the lesser force is:

Step-by-step explanation:

The masses of protons and electron, and the distance between them are given below.

`\begin{gathered} m_p=1.67*10^(-11)kg \\ \\ m_e=9.11*10^(-31)kg \\ \\ r=4.67*10^(-11)kg \\ \\ G=6.67*10^(-11)m^3kg^(-1)s^(-2) \end{gathered}`

The gravitational force between the proton and electron is calculated below

`\begin{gathered} F_g=(Gm_1m_2)/(r^2) \\ \\ F_g=(6.67*10^(-11)*1.67*10^(-27)*9.11*10^(-31))/((4.67*10^(-11))^2) \\ \\ F_g=4.65*10^(-47)N \end{gathered}`

The magnitude of the charge on a proton and an electron is the same, and is given as:

`\begin{gathered} q_p=1.6*10^(-19)C \\ \\ q_e=1.6*10^(-19)C \end{gathered}`

The electrostatic force between the proton and electron is then calculated as:

`\begin{gathered} F_E=(kq_pq_e)/(r^2) \\ \\ F_E=(9*10^9*1.6*10^(-19)*1.6*10^(-19))/((4.67*10^(-11))^2) \\ \\ F_E=1.056*10^(-7)N \end{gathered}`

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:

`\begin{gathered} (F_E)/(F_g)=(1.056*10^(-7))/(4.65*10^(-47)) \\ \\ (F_E)/(F_g)=2.27*10^(39) \end{gathered}`