The radial wave equation for hydrogen atom is ψ = 1 16 4 1 a ο 3 2 x ⁡ - 1 x 2 ⁡ - 8 x ⁡ + 12 e - x 2 where x = 2 r a o , a ο = radius of first bohr's orbit the minimum and maximum position of radial nodes from nucleus are:

Step-by-step solution

For node ψ 2 = 0 , So also Ψ = 0 So for: ψ = 1 16 4 1 a ο 3 2 x ⁡ - 1 x 2 ⁡ - 8 x ⁡ + 12 e - x 2 x ⁡ - 1 x 2 ⁡ - 8 x ⁡ + 12 should be equal to zero x ⁡ - 1 x 2 ⁡ - 8 x ⁡ + 12 = 0 , solve the equation x ⁡ - 1 x 2 ⁡ - 8 x ⁡ + 12 X = 1 , 2 , 6 i . e . r = 0.5 a ο , a ο , 3 a ο ; ∵ x = 2 r a ο So minimum 0.5 a ο maximum 3 a ο