Let `lambda_(alpha), lambda_(beta),and lambda'_(alpha)` denote the wavelength of the X-ray of the `K_(alpha), K_(beta), and L_(alpha)` lines in the characteristic X-rays for a metal. Then.

Options

A. `lamda_alpha gt lamda'_(alpha)gtlamda_beta`
B. `lamda'_alpha gt lamda'_(beta)gtlamda_alpha`
C. `1/lamda_(beta)=1/lamda_(alpha)+1/(lamda'_(alpha))`
D. `1/lamda_(alpha)=1/lamda_(beta)+1/(lamda'_(alpha))`

Answer

C

Explanation

Since, `lamda prop 1/(DeltaE)`
`DeltaE =` Energy radiated when `e^(-)` jumps from higher energy orbit to lower energy orbit.
`(DeltaE)_(kbeta)gt (DeltaE)_(kalpha)gt(DeltaE)_(Lalpha)`
`:. lamda_(alpha) gt lamda_(alpha) gt lamda_(beta) `
Also, `(DeltaE)_(kbeta)= (DeltaE)_(kalpha)+(DeltaE)_(Lalpha)`
`implies (hc)/(lamdabeta)=(hc)/(lamdaalpha)+(hc)/(lamdaalpha)implies1/(lamdabeta)=1/(lamdaalpha)+1/(lamdaalpha)`