If the difference between (n + 1)^ th Bohr radius and n^ th Bohr radius is given by (n - 1)^ th Bohr radius, then the value of n is

Step-by-step solution

The radius of the n^ th Bohr orbit is given by r_n = r₀ n^2 , where r₀ is the radius of the first Bohr orbit. According to the given condition: r_ n+1 - r_n = r_ n-1 Substituting r_n = r₀ n^2 : r₀ (n+1)^2 - r₀ n^2 = r₀ (n-1)^2 Dividing both sides by r₀ : (n+1)^2 - n^2 = (n-1)^2 n^2 + 2n + 1 - n^2 = n^2 - 2n + 1 2n + 1 = n^2 - 2n + 1 n^2 - 4n = 0 n(n - 4) = 0 Since n must be a positive integer, n = 4 .