By assuming Bohr's postulates derive an expression for radius of nth orbit of electron, revolving round the nucleus of hydrogen atom.
Let the electron of mass m revolves around a nucleus (H-atom) in an orbit of radius rn with linear velocity vn.
As the electron revolves in an stationary orbit, thus centrifugal force acting on the electron is balanced by the coulombic force i.e. Fcentrifugal=Fcoulomb
∴ mv2nrn=ke2r2n where k=14πϵo=9×109
⟹ rn=ke2mv2n
Also we use mvnrn=nh2π
Eliminating vn from both equations, we get rn=ke2m.4π2m2r2nn2h2
⟹ rn=h2n24π2mke2
Putting m=9.1×10−31kg, h=6.626×10−34Js and e=1.6×10−19C
We get radius of nth Bohr orbit rn=0.529 n2 Ao