The radius of the orbit of an electron in Hydrogen-like aton is 4.5 `alpha_0` where `alpha_0` is the Bohr radius. Its orbital angular momentum is `(3h)/(2pi)`. 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)

Options

A. `(9)/(32R)`
B. `(9)/(16R)`
C. `(9)/(5R)`
D. `(4)/(3R)`

Answer

A, C

Explanation

`R_(n)=4.5a_(0)`
`L=mvr=(3h)/(2pi)[as n=3,z=2]`
`(1)/(lambda)=Rz^(2)((1)/(n_(f)^(2))-(1)/(n_(1)^(2)))`
`(1)/(lambda_(3rarr1))=R4[(1)/(1)-(1)/(9)]=4R(8)/(9) rArrlambda_(3rarr1)=(9)/(32R)`
`(1)/(lambda_(2rarr1))=R4[(1)/(1)-(1)/(4)]=(3)/(4)R rArrlambda_(2rarr1)=(1)/(3R)`
`(1)/(lambda_(3rarr2))R4[(1)/(4)-(1)/(9)]=(5)/(36)4R rArrlambda_(3rarr2)=(9)/(5R)`