Question

Derive a formula for radius of the stable orbit of hydrogen atom on the basis of Bohr model. Prove that in hydrogen atom the ratio of the stable radius are 1: 4: 9

Answer 1

Bohr’s Radius or Radii of Stable Orbits
Suppose for an atom the radius of nth orbit is r_n and in this a electron is moving with the speed of v. If the electron has a mass of m, then acquisition by Bohr
mv_nr_n = \(n \frac{h}{2 \pi}\) ……………… (1)
From first condition of Bohr
F_e = F_c

r_n = n² r₁, r₁ = 0.53 Å where Z = 1, for the hydrogen atom.
Where n = 1, 2, 3 ……..
r₁ : r₂ : r₃ = (i)²r₁ : (2)²r₁ : (3)²r₁
r₁ : r₂ : r₃ = 1: 4 : 9 ………..