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The average separation between the proto...

The average separation between the proton and the electron in a hydrogen atom in ground state is `5.3xx10^-11m`. a. Calculate the Coulomb force between them at this separation.

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The correct Answer is:
A, B
Let `F_e and F_G` are electric force and gravitatioN/Al force between two protons
`:. F_e/F_g= (9xx10^9xx(1.6)^2xx10^-38)/r^2/(6.67xx10^011xx(1.732)^2xx10^-54)/r^2`
`= (9xx(106)^2xx10^-29)/(6.67xx(1.732)^2xx10^-65)`
` 1.24xx10^36`
Average separationbetween proton and electron of Hydrogn atom
`r=5.3xx10^-11m`
a. Coulomb's force,
`F=9xx10^9xx(q_1q_2)/r^2`
(9xx10^9xx(1.0xx10^-19)^2)/(5.3xx10^-11)^2)`
b. When the average distance between proton and electron becomes 4 times that of its ground state, then
Coulomb's force
`F= 1/(4pi epsilon_0) (q_1 q_2)/((4)^2)`
`=(9xx10^9xx(1.6xx10^-19)^2)/(16xx(5.3)^2xx10^-22)`
` (9xx(1.6)^2)/(10xx(5.3)^2) xx10^-7`
`=0.0512xx10^-7`
`=5.1xx10^-9N`
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