Obtain an expression for the radius of Bohr orbit for H atom.

Explanation

Consider an electron of hydrogen atom revolving aroud the n8cleus in circular orbit of radius r. Let m and 3e be the mass and charge of the electyron and v be the linear speed of the electron. According to Boht's first postulate,
centripetal force = electrostatic force of attraction
`(mv^2)/r=1/(4piepsi_(0))e^2/r^2`
`v^2=e^2/(4piepsi_(0)"mr")" ...(i)"`
According to Bhar's `2^("nd")` postulate,
angular momentum `=n h/(2pi)`
`"mvr"=nh/(2ip)` ltbr4gt `v=(nh)/(2pi"mr")" ...(ii)"`
`"or "v^2=(n^2h^2)/(4pi^2m^2r^2)" ...(iii)"`
Comparing equation (i) and equation (iii), We get
`e^2/(4piepsi_(0)"mr")=(n^2h^2)/(4pi^2m^2r^2)`
`"or "r=((h^2epsi_(0))/(pime^(2)))n^2`
This eaution gives the radius of `n^("th")` Both orbit for Hatom.
Radius of Both's orbit of hydrogen atom is directly propo4rtional to the square of principal quantum number.