Question

Use de-Broglie's hypothesis to write the
relation for the nth radius of Bohr orbit in
terms of Bohr's quantization condition of
orbital angular momentum.​

Answer 1

The relation of the orbit will be - a0 = h²/4π²mkze²

According to de-Broglie's hypothesis wavelength is λ = hmv

Bohr suggested quantizing the angular momentum of the electrons that surround the atom -

mvr = nh/2π

v = nh/2πmr

As, the circular motion is balanced by electrostatic forces, thus -

kze²/r² = mv²/r

mv² = kze²/r

mn²h²/4π²m²r² =  kze²/r

r = n²h²/ 4π²mkze²

r = a0n² where a0 is the Bohr radius

Thus, a0 = h²/4π²mkze²