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/2π. 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) 916R, 95R, 43R, 932R
932R
916R
95R
43R
Solution:
Given data:4.5a0=a0n2Z... (i)nh2π=3h2π. (ii)So,n=3andz=2So, possible wavelength are:1λ1=RZ2[11232]⇒λ1=932R1λ2=RZ2[11222]⇒λ2=13R1λ3=RZ2[12232]⇒λ3=95R