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 `2 z - 1`.
B. The atomic number of first impurity is `2 z + 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

Moseloey's law: `lambda prop (1)/((z - 1)) 2: (lambda_(z))/(lambda_(1)) = ((z_(1) - 1)^(2))/((z - 1)^(2))`
`z_(1) - 1 = (z - 1) 2`:
`z_(1) = 2z -1: (lambda_(z))/(lambda_(2)) = (1)/(4) = ((z_(2) - 1)/(z - 1))^(2)`