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

Explanation

total energy of the electron in hydrogen atom is `-13.6 eV =- 13.6 xx 1.6 xx 10^(-19) J=- 2.2 xx 10^(-18) J`
we have ` E=-(e^2 )/( 8 pi epsi_0 r ) =- 2.2 xx 10^(-18) J`
` therefore r= (e^2)/( 8pi epsi_0 E ) = (( 9xx 10^9 )(1.6 xx 10^(-19))^2)/( (2)(-2.2 xx 10^(-18))) = 5.3 xx 10^(-11) m`
` v= (e )/(sqrt(4 pi epsi_0 m r ) )= ( 1.6 xx10^(-19))/(sqrt(4xx pi xx 8.85 xx 10^(-12) xx 9.1 xx 10^(-31) xx 5.3 xx 10^(-11))) = 2.2 xx 10^(6) ms^(-1)`