The radius of the orbit of an electron in a Hydrogen - like atom is `4.5s_(0)` where `a_(0)` is the bohr radius its orbital angular momentum is `(3h)/(2 pi) ` it is given that is is plank constant and R is rydberg constant .The possible wavelength `(s)` , when the atom de- excite , is (are)

Options

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

Answer

A, C

Explanation

`R_(n)=4.5 a_(0)`
`L=mvr=(3h)/(2pi)["as" n=3,x=2]`

`(1)/(lamda)=Rz^(2)((1)/(n_(f)^(2))-(1)/(n_(1)^(2)))`
`(1)/(lamda_(3 rarr 1))R4[(1)/(1)-(1)/(9)]=4R (8)/(9) rArr lamda_(3 rarr1)=(9)/(32 R)`
`(1)/(lamda_(2 rarr1))=R4[(1)/(1)-(1)/(4)]=(3)/(4) 4RrArr lamda_(2 rarr1)=(1)/(3R)`
`(1)/(lamda_(3 rarr2))=R4[(1)/(4)-(1)/(9)]=(5)/(36) 4R rArr lamda_(3 rarr 2) = (9)/(5R)`.