The radius of the orbit of an electron in a hydrogen like atom is 4.5a₀ , where a₀ is the Bohr radius. Its orbital angular momentum is 3h 2 . It is given than h is Planck's constant and R is Rydberg's constant. The possible wavelength ( ) , when the transition of atom from higher energy level to lower energy level, is

Step-by-step solution

The orbital angular momentum of an electron is given by L = nh 2 . Given L = 3h 2 , we get n = 3 . The radius of the n -th orbit in a hydrogen-like atom is r = n^2 Z a₀ . Substituting r = 4.5a₀ and n = 3 : 4.5a₀ = 3^2 Z a₀ Z = 9 4.5 = 2 The possible transitions from the n = 3 state to lower energy levels are n = 3 1 and n = 3 2 . Using the Rydberg formula for wavelength: 1 = RZ^2 ( 1 n_f^2 - 1 n_i^2 ) For the transition n = 3 1 : 1 = R(2)^2 ( 1 1^2 - 1 3^2 ) = 4R ( 1 - 1 9 ) = 4R ( 8 9 ) = 32R 9 = 9 32R For the tra