Question

Which force is the more dominant one in the hydrogen atom, the gravitational or the electrical? by what factor?

Answer 1

The electrical is dominant.
In the hydrogen atom, the electrical force is vastly stronger than the gravitational. It is roughly 39 orders of magnitude greater, i.e. ratio of the electrical to gravitational force is on the order of 10^39.

Answer 2

Electrical Force by a factor of
`2.23 * 10^(39)`

Step-by-step explanation:

Known values

magnitude of the charge of an electron |e| =
`1.6 * 10^(-19)`

magnitude of the charge of a proton |e| =
`1.6 * 10^(-19)`

Note: magnitude means we only consider positive numerical value

mass of an electron m =
`9.1  * 10^(-31)` kg

mass of an electron M =
`1.7 * 10^(-27)` kg

`Electric force,F_e = (ke^(2))/(r^(2))`

`Gravitational force,F_g = (GMm)/(r^(2) )`

`(Electric force )/(Gravitational force)  = ((ke^(2))/(r^(2)))/( (GMm)/(r^(2) )) \\\\(Electric force )/(Gravitational force)  = (ke^2)/(GMm) \\\\(Electric force )/(Gravitational force)  = (9 * 10^9 * (1.6 * 10^(-19))^2)/(6.67 * 10^(-11) * 1.7 * 10^(-27) * 9.1 * 10^(-31)) \\\\(Electric force )/(Gravitational force)  = 2.23 * 10^(39)`