A cobalt target `(Z = 27)` is bomberded with electron and the wavelength of its characteristic spectrum are measured . A second , fainter characcteristic spectrum is also found because of an impurity in the target. The wevelength of the `K_(alpha)` lines are 178.9 pm (cobalt) and `143.5 pm` (impurity). What is the impurity?

Explanation

Using Moseley's law and putting `c//lambda` for `v` ( and assuming `b=1`), we obtain
`sqrt((c )/(lambda_(c_(0))))aZ_(c_(0))-a`
and `sqrt((c )/(lambda_(x)))aZ_(x)-a`
Dividing yields
`sqrt((lambda_(c_(0)))/(lambda_(x)))=(Z_(x)-1)/(Z_(c_(0)-1))`
Substituting gives us
`sqrt((178.9"pm")/(143.5"pm"))=(Z_(x)-1)/(27-1)`
Solving for the unknown, we find `Z_(x)=30.0`, the impurity zinc.