Question

A tissue paper soaked with polluted water showed $K_{\alpha }$ peaks at 78.9 pm, 146 pm, 158 pm and 198 pm. Find the elements it contained.

Answer 1

The frequency (f) of the $K_{\alpha }$ line is related to the atomic number Z by the following relation:

$f=\frac{c}{\lambda }=2.48\times {10}^{15}(Z-1{)}^{2}Z=1+\sqrt{\frac{c}{\lambda \times 2.48\times {10}^{15}}}=1+\sqrt{\frac{3\times {10}^8}{78.9\times {10}^{-12}\times 2.48\times {10}^{15}}}=40,i.e.,ZrZ=1+\sqrt{\frac{3\times {10}^8}{146\times 2.48\times {10}^{-3}}}=30.1,i.e.,ZnZ=1+\sqrt{\frac{3\times {10}^8}{158\times 2.48\times {10}^{-3}}}=29,i.e.,CuZ=1+\sqrt{\frac{3\times {10}^8}{198\times 2.48\times {10}^{-3}}}=26,i.e.,Fe$