Radius of `3^(rd)` orbit of `Li^(2+)` ion is x cm then which is not the de Broglie wavelength of electrons in the first orbit is (in cm)

Options

A. `6pix `
B. `(2pi x)/(9)`
C. `(2pi x )/(3)`
D. `(8pi x)/(3)`

Answer

A, B, C

Explanation

`r prop (n^2)/(Z) , (r_1)/(r_3) = (n_1^2)/(n_2^2) = 1/(3^2) = 1/9 , r_1 = x/9 [therefore r_3 = x]`
`therefore 2 pi r = n lambda`
`therefore 2 pi xx x/9 = 1 xx lambda = (2pi x)/(9)`