Question

If `13.6eV` energy is required to separate a hydrogen atom into a proton and an electron, then the orbital radius of electron in a hydrogen atom is
A. `5.3xx10^(-11)m`
B. `4.3xx10^(-11)m`
C. `6.3xx10^(-11)m`
D. `7.3xx10^(-11)m`

Answer 1

Correct Answer - A
Here, `E=-13.6eV=-13.6xx1.6xx10^(-19)=-2.2xx10^(-18)J`
`E=(-e^2)/(8piepsilon_0r)`
`therefore` As orbital radius,
`r=(-e^2)/(8piepsilon_0E)=(9xx10^(9)xx(1.6xx10^(-19))^2)/(2xx(2.2xx10^(-18)))=5.3xx10^(-11)m`.