It is found expertimentally that 13.6eV energy is required to separated a hydrogen atom into a proton and an electron. Compute the orbital radius and velocity of electron in a hydrogen atom.

Explanation

Here, total energy of electron
`E=-13.6eV=-13.6xx1.6xx10^(-19)J`
`=-2.2xx10^(-18)J`
form `E=(-e^2)/(8pi in_0r)`
`r=(-e^2)/(2(4pi in_0r)E)=(-9xx10^(-19)xx(1.6xx10^(-19))^2)/(2(-2.2xx10^(-18)))`
`=5.3xx10^(-11)m`
velocity, `v=e/(sqrt(4pi in_0 mr))`
Where `m=9.1xx10^(-31)kg`
`:. v=(1.6xx10^(-19))/(sqrt((9.1xx10^(-31)xx5.3xx10^(-11))/(9xx10^9)))`
`=2.2xx10^6m//s`