A The wavelength of the `K_alpha` line ofthe characteristic X rays emitted by an element is 0.64 Å . What is the wavelength of `K_beta` line emitted by the same element?

Options

A. a. 0.18 Å
B. b. 0.27 Å
C. c. 0.54 Å
D. d. 0.72 Å

Answer

C

Explanation

In this case, `n_i =2,3,4,…. " and " n_f =1`
`(1)/(lamda_(K_alpha)) = R (Z -1)^2 [(1)/(1^2) - (1)/(2^2) ] = 3/4 K`
where K =R `(Z-1)^2`
Similarly, `(1)/(lamda_(K_beta)) = K[(1)/(1^2) - (1)/(3^2) ] = 8/9 K`
`therefore (lamda_(K_beta))/(lamda_(K_alpha)) = (3K)/(4) xx (9)/(8K) = 27/32`
`therefore lamda_(K_beta) = 27/32 xx 0.64= 0.54 Å`