Question

The most common isotope of hydrogen contains a proton and an electron 'separated by about -11-27 5.0 x 10 m. The mass of proton is approximately 1.7 x 10 kg. The mass of the electron is -31 approximately 9.0 x 10 kg. a) Use Newton's law of universal gravitation to calculate the gravitational force between the electron and proton in the hydrogen atom. -19 b) Use 1.6 x 10 C as the elementary unit of charge to determine the force of attraction between the two particles. How many orders of magnitude greater is the electric force between the two particles than the gravitational force between the two particles

Answer 1

A) F_g = 4.05 10⁻⁴⁷ N, B) F_e = 9.2 10⁻⁸N, C)
`(F_e)/(F_g)` = 2.3 10³⁹

Step-by-step explanation:

A) It is asked to find the force of attraction due to the masses of the particles

Let's use the law of universal attraction

F =
`G (m_1m_2)/(r^2)`

let's calculate

F =
`6.67 \ 10^(-11) \ (9.1 \ 10^(-31) \ 1.67 \ 10 ^(-27) )/((5 \ 10^(-11))^2 )`

F_g = 4.05 10⁻⁴⁷ N

B) in this part it is asked to calculate the electric force

Let's use Coulomb's law

F =
`k \ (q_1q_2)/(r^2)`

let's calculate

F =
`9 \ 10^9 \ ((1.6 \ 10^(-19) )^2)/((5 \ 10^(-11))^2)`

F_e = 9.2 10⁻⁸N

C) It is asked to find the relationship between these forces

`(F_e)/(F_g) = (9.2 \ 10^(-8) )/(4.05 \ 10^(-47) )`

= 2.3 10³⁹

therefore the electric force is much greater than the gravitational force