Concept of X- rays

Question

Let !!lambda_alpha, lambda_beta and lambda_alpha^'!! denote the wavelengths of the !!X-!!rays of the !!K_alpha, K_beta!! and !!L_alpha!! lines in the characteristic !!X-!!rays for a metal.

a) !!lambda_alpha^' > lambda_alpha > lambda_beta!!

b) !!lambda_alpha^'> lambda_beta > lambda_alpha!!

c) !!1/(lambda_beta) + 1/(lambda_alpha)= 1/ (lambda_alpha^'!!

d) !!1/(lambda_beta)= 1/(lambda_alpha) + 1/ (lambda_alpha^'!!

Solution:

!!E_K- E_L = (hc)/(lambda_alpha)!!

!!E_K- E_M = (hc)/(lambda_beta)!!

!!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)> (E_K- E_L) > (E_L- E_M)!!

!!(hc)/(lambda_beta) > (hc)/(lambda_alpha)>(hc)/(lambda_alpha^')!!

!!=> 1 /(lambda_beta) > 1/(lambda_alpha)>1/(lambda_alpha^')!!

Therefore, options (A) and (D) are correct.