X-ray from a tube with a target `A` of atomic number `Z` shows strong `K` lines for target `A` and weak`K` lines for impurities. The wavelength og `K_(alpha)` lines is `lambda_(z)` for target `A` and `lambda_(1) and lambda_(2)` for two impurities.
`(lambda_(z))/(lambda_(1)) = 4 and (lambda_(z))/(lambda_(2)) = (1)/(4)`
Assuming the screeining contant of `K_(alpha)` lines to be unity select the correct statement(s).

Options

A. The atomic number of first impurity is `2Z -1`
B. The atomic number of first impurity is `2Z +1`
C. The atomic number of second impurity is `(Z +1)/(2)`
D. The atomic number of second impurity is `(Z)/(2)+1`

Answer

A, C

Explanation

`{:((lamda_(0))/(lamda_(1))=4,rArr,((Z_(1)-1)^(2))/((Z-1)^(2))=4),(,rArr,Z_(1)=2Z-1),((lamda_(0))/(lamda_(2))=(1)/(4),rArr,((Z_(2)-1)^(2))/((Z-1)^(2))=(1)(1)/(2)),(,rArr,Z_(2)=(Z+1)/(2)):}`