According to the Bohr model, the ratio of the planar area enclosed by the 2^ nd orbit of a Li ²⁺ ion to the planar area enclosed by the 4^ th orbit of a Be ³⁺ ion is

Step-by-step solution

The radius of the n^ th Bohr orbit is given by r n^2 Z . The planar area enclosed by a circular orbit is A = r^2 . Therefore, the area is proportional to the square of the radius: A ( n^2 Z )^2 = n^4 Z^2 For the Li ²⁺ ion, Z = 3 and n = 2 . The area of its 2^ nd orbit is: A₁ 2^4 3^2 = 16 9 For the Be ³⁺ ion, Z = 4 and n = 4 . The area of its 4^ th orbit is: A₂ 4^4 4^2 = 256 16 = 16 The ratio of the two areas is: A₁ A₂ = 16 9 16 = 1 9 Thus, the ratio of the areas is 1 : 9 . Answer: 1 : 9