Suppose A_n represents the area enclosed by the n th orbit of a hydrogen atom. A plot of (A_n/A₁) versus (n)

Step-by-step solution

The radius of the n th Bohr orbit of a hydrogen atom is given by r_n = r₁ n^2 , where r₁ is the radius of the first orbit. The area enclosed by the n th orbit is A_n = r_n^2 . Substituting the expression for r_n , we get A_n = (r₁ n^2)^2 = r₁^2 n^4 . Since the area of the first orbit is A₁ = r₁^2 , we can write A_n = A₁ n^4 . Rearranging the terms, we get A_n A₁ = n^4 . Taking the natural logarithm on both sides, we obtain ( A_n A₁ ) = (n^4) = 4 (n) . Comparing this with the equation of a straight line y = mx + c ,