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The radius of the orbit of an electron i...

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)

A

`(9)/(32 R)`

B

`(9)/(16 R)`

C

`(9)/(5 R)`

D

`(9)/(3 R)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`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)`.
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