Question

Find the force (in N) of electrical attraction between a proton and an electron that are 6.4 ✕ 10−11 m apart. answer in:______NCompare this to the gravitational force between these particles. (Enter the gravitational force, in N.) answer in:_______N

Answer 1

Given:

The distance between electron and proton is

`r=6.4*10^(-11)\text{ m}`

Required:

The Coulomb's force and gravitational force.

Step-by-step explanation:

The Coulomb's force between electron and proton can be calculated by the formula

`F_c=k(|q_eq_p|)/(r^2)`

Here, k is the constant whose value is

`k\text{ = 9}*10^9\text{ N m}^2\text{ /C}^2`

The charge of an electron is

`q_(_e)=-1.6*10^{-19\text{ }}C`

The charge of the proton is

`q_p=\text{ 1.6}*10^(-19)\text{ C}`

On substituting the values, Coulomb's force will be

`\begin{gathered} F_c=(9*10^9*1.6*10^(-19)*1.6*10^(-19))/((6.4*10^(-11))^2) \\ =5.625*10^(-8)\text{ N} \end{gathered}`

The gravitational force can be calculated by the formula

`F_g=(Gm_em_p)/(r^2)`

Here, G is the universal gravitational constant whose value is

`G\text{ = 6.67}*10^(-11)\text{ N m}^2\text{ /kg}^2`

The mass of the electron is

`m_e=9.1*10^(-31)\text{ kg}`

The mass of the proton is

`m_p=1.67*10^(-27)\text{ kg}`

On substituting the values, the gravitational force will be

`\begin{gathered} F_g=(6.67*10^(-11)*9.1*10^(-31)*1.67*10^(-27))/((6.4*10^(-11))^2) \\ =2.47*10^(-47)\text{ N} \end{gathered}`

Final Answer: Coulomb's force is 5.625e-8 N

Gravitational force is 2.47e-47 N