The innermost orbit has lowest possible radius in hydrogen atom and is equal to ao, Bohr's radius.That is when hydrogen atom is formed, the orbital electron cannot be brought closer to nucleus with an inetermediate distance less than ao. This can be proved form the Bohr's postulates
From the first Bohr's postulate on angular momentum of the orbital electron mn^2vn^2 rn^2 = n^2h^2/ 4π^2 and from the second Bohr's postulate stating the equivalence of nuclear attractive force with the centrifugal force mn vn^2 rn = e^2/K.
Dividing one by the other, mn rn = n^2 h^2 εo/π e^2 or mn = n^2 h^2 εo/π e^2 rn
mn rn = [mo/(1- vn^2/c^2)^1/2][n^2ao (1- vn^2/c^2)^1/2] = n^2 mo ao or mn = n^2 mo ao / rn
From Bohr's radius ao = h^2 εo/ moπ e^2 . mo = h^2 εo/π e^2 ao. The relativistic increase of mass cannot be less than zero. i.e., dm = mn - mo ≃(1/2)mo vn^2 /c^2 = [h^2 εo/π e^2] [ n^2/rn - 1/ao ] . The highest possible value of n^2/rn = 1/r1 , since dm can not be negative r1 = ao . The lowest possible radius of the orbital electron in hydrogen atom is ao
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