The ratio of the first three radii of Bohr's atom is:

Step-by-step solution

The radius of the n^ th orbit in a Bohr atom is given by the formula r_n = a₀ n^2 Z , where a₀ is the Bohr radius, n is the principal quantum number, and Z is the atomic number. For a given atom, a₀ and Z are constants. Therefore, the radius is directly proportional to the square of the principal quantum number, r_n n^2 . The first three radii correspond to n = 1, 2, 3 . Calculating the ratios: r₁ : r₂ : r₃ = 1^2 : 2^2 : 3^2 r₁ : r₂ : r₃ = 1 : 4 : 9 . Answer: 1: 4: 9