Derive an expression for the radius of `n^(th)` Bohr's orbit of hydrogen atom hence write the expression for the radius of first orbit of hydrogen atom.

Explanation

For the electron, we have
From Bohr.s Postulate, `mvr=(pih)/(2pi)` and For Rutherford.s Model,
`(mv^(2))/(r)=(1)/(4piepsi_(0)).(Ze^(2))/(r^(2))`
`:.m^(2)v^(2)r^(2)=(n^(2)h^(2))/(4pi^(2))`
and `mv^(2)r=(1)/(4piepsi_(0))Ze^(2)`
`:.r=(n^(2)h^(2)xx4piepsi_(0))/(4pi^(2)xxZe^(2)m)`
Bohr.s radius (for n=1) `=(h^(2)epsi_(0))/(piZe^(2)m)`.