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. `lambda_(alpha) gt lambda_(alpha) gt lambda_(beta)`
B. `lambda_(alpha) gt lambda_(beta) gt lambda_(alpha)`
C. `(1)/(lambda_(beta)) = (1)/(lambda_(alpha)) + (1)/(lambda'_(alpha))`
D. `(1)/(lambda_(alpha)) = (1)/(lambda_(beta)) + (1)/(lambda_(alpha))`

Answer

A, C

Explanation

`E_(K) - E_(L) = (hc)/(lambda_(alpha))` (i)

`E_(K) - E_(M) = (hc)/(lambda_(beta))` (ii)
`E_(L) - E_(M) = (hc)/(lambda'_(alpha))` (iii)
(ii) - (i) ` implies E_(L) - E_(M) = (hc)/(lambda'_(alpha)) = (hc)/(lambda_(beta)) - (hc)/(lambda_(alpha))`
`(1)/(lambda_(beta)) = (1)/(lambda_(alpha)) + (1)/(lambda'_(alpha))`
Also, `(E_(K)) - E_(M)) gt (E_(K) - E_(L)) gt (E_(L) - E_(M))`
`(hc)/(lambda_(beta)) gt (hc)/(lambda_(alpha)) gt (hc)/(lambda'_(alpha))`