If the frequency of `K_(alpha), K_(beta)` and `L_(alpha)` , X-ray lines of a substance are `v_(K_(alpha)), v_(K_(beta))`, and `v_(L_(beta))`

Options

A. `v_(K_(beta))=v_(K_(alpha))+v_(L_(alpha))`
B. `v_(K_(beta))=v_(K_(alpha))-v_(L_(alpha))`
C. `v_(K_(beta))=(v_(K_(alpha)))/(v_(L_(alpha)))`
D. `v_(K_(beta))^(2)=(v_(K_(alpha))*v_(L_(alpha)))/(2)`

Answer

A

Explanation

As energy of `K_(alpha)` X-rays is
`" " E_(K_(alpha))=E_(K_(beta))-E_(L)" " ....(i)`
`" " E_(K_(betaa))=E_(K_(alpha))+E_(L_(alpha))" " ....(iii)`
On adding Eq. (i) and Eq. (ii)
`:. " " hv_(K_(beta))=hv_(K_(alpha))+hv_(L_(alpha))" "[E =hv]`
or `" " v_(K_(beta))=v_(K_(alpha))+K_(L_(alpha))`