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

Answer

A, C

Explanation

Given data `4.5_(alpha_0)=alpha_0(n^2)/(Z)`
`(nh)/(2pi)=(3h)/(2pi)`
So `n=3` and `z=2`
So possible wavelength are
`(1)/(lamda_1)=RZ^2[(1)/(1^2)-(1)/(3^2)]implieslamda_1=(9)/(32R)`
`(1)/(lamda_2)=RZ^2[(1)/(1^2)-(1)/(2^2)]implieslamda_2=(1)/(3R)`
`(1)/(lamda_3)=RZ^2[(1)/(2^2)-(1)/(3^2)]implieslamda_3=(9)/(5R)`