The radius of the orbit of an electron in a Hydrogen-like atom is 4.5 a 0 , where a 0 is the Bohr radius. Its orbital angular momentum is 3 h 2 π . It is given that h is Planck's constant and R is Rydberg constant. the possible wavelength (s), when the atom de-excites, is (are)

Step-by-step solution

R n = 4.5 a 0   ⇒   a 0 n 2 / z = 4.5  a 0 ∴    n = 3 ,  z = 2 L = mvr = 3 h 2 π as n = 3 , z = 2 1 λ = Rz 2 1 n f 2 - 1 n 1 2 1 λ 3 → 1 = R 4 1 1 - 1 9 = 4 R 8 9 ⇒ λ 3 → 1 = 9 3 2 R 1 λ 2 → 1 = R 4 1 1 - 1 4 = 3 4 4 R ⇒ λ 2 → 1 = 1 3 R 1 λ 3 → 2 = R 4 1 4 - 1 9 = 5 3 6 4 R ⇒ λ 3 → 2 = 9 5 R