Question

Compare the electrostatic force between an electron and proton separated by 0.530x10^-10m with the gravitational force between them. This distance is their average separation in a hydrogen atom (r=0.530x10^-10m)

Answer 1

The electrstatiel force between two charges q1 and q2 separated by distance r is-

F_{​​​​​​e}=kq1q2/r^{​​​​​2}

where k=9x10⁹N-m²/c^{​​​​​​2}​​​

q1=charge on electron =-e

q2=charge on proton=+e

r=0.53x10^-10m

q1 and q2 are opposite sign ,so force is attractive.

Where e=1.6x10^-19c

F_{​​​​​​e}=9x10⁹x(1.6x10^-19)²/(0.53x10^-10)²=8.2x10^-8Newton

mass of electron m1=9.11x10^-31kg

Mass of proton m2=1.67x10^-27kg

The gravitational force-

F_{​​​​​​g}​​​​​=Gm1m2/r^{​​​​​​2}

Where G is gratitational constant=6.674x10^-11N-m²/kg^{​​​​​2}

F_{​​​​​​g=}​​​​(6.674x10^-11x9.11x10^-31x1.67x10^-27)/(0.53x10^-10)²

^F_{​​​​​​g}​​​​​​​​​​=3.6x10^-47N

F_​e/F_{​​​​​​g =}(8.2x10^-8)/(3.6x10^-47)=2.28x10³⁹N

so electrostatic force is 2.28x10³⁹ times of gravitational force.