An electron and a proton are separated by a distance of 1.8 Times 110^-10 m (rou

Question

An electron and a proton are separated by a distance of 1.8 Times 110^-10 m (roughly the diameter of a single atom). What is the magnitude of the electric interaction between the electron and the proton? magnitude of electric force = What is the magnitude of the gravitational interaction between the electron and the proton? magnitude of gravitational force In this scenario, how many times stronger is the electric force than the gravitational force? The electric force is times stronger than the gravitational force.

Explanation / Answer

Given: q1 = ( + proton charge ) = + 1.60 x 10 ^ -19 C
q2 = ( - electron charge) = - 1.60 x 10 ^ -19 C
mp = ( mass of proton ) = 1.67 x 10 ^ -27 kg
me = ( mass of electron ) = 9.11 x 10 ^-31 kg
d = 1.8 x 10 ^-10 m
k = 9.0 x 10^9 N * m^2 / C^2
G = 6.67 x 10 ^-11 N * m^2/ kg^2

Find: Fe ( electrostatic force ) and Fg ( gravitational force )


Solution: Fe = k * q1 * q2 / d ^2

Fe = ( 9.0 x 10 ^9 N * m^2/ C^2 ) ( +1.6 x 10^-19 C ) ( -1.6 x 10^-19 C) / ( 1.8 x 10 ^-10 m )^2

Fe = ( 9.0 x 10^9 N * m^2/ C^2 ) ( -2.56 x 10 ^-38 C^2 ) / ( 1.8 x 10 ^-10 m ) ^2

Fe = -23.0 x 10^ -29 N / 3.24 x 10 ^-20

Fe = - 7.1 x 10 ^-9 N



Solution: Fg = G * mp * me / d ^2


Fg = ( 6.67 x 10 ^-11 N * m^2/kg^2 ) ( 1.67 x 10 ^ -27kg ) ( 9.11 x 10 ^ -31 kg ) / ( 1.8 x 10 ^-10 m )^2

Fg = ( 6.67 x 10^-11 N * m^2/kg^2 ) ( 15.21 x 10^-58 kg^2 )
/ ( 3.24 x 10^-20 m^2 )

Fg = 101.5 x 10^-69 N / 3.24 x 10^-20

Fg = 31.32 x 10^-49 N


How much stronger is the electrostatic forces of the system than those of the gravitational forces?


Fe / Fg = 7.1 x 10^-9 N / 31.32 x 10^-49 N
= 0.2266 x 10^40 times more stronger.

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