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Question:

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[112𕒵32]⇒λ1=932R1λ2=RZ2[112𕒵22]⇒λ2=13R1λ3=RZ2[122𕒵32]⇒λ3=95R