Question

X-ray from a tube with a target A of atomic number Z shows strong $K_{\alpha }$ lines for target A and two weak $K_{\alpha }$ lines for impurities. The wavelength of $K_{\alpha }$ lines is ${\lambda }_0$ for target A and ${\lambda }_1$ and ${\lambda }_2$ for two impurities respectively.$\frac{{\lambda }_0}{{\lambda }_1}=4$ and $\frac{{\lambda }_0}{{\lambda }_2}=\frac{1}{4}$. The screening constant of $K_{\alpha }$ lines is unity. Select the correct alternative(s) :

• A. The atomic number of first impurity is $2Z-1$
• B. The atomic number of second impurity is $\frac{Z+1}{2}$
• C. The atomic number of first impurity is $2Z+1$
• D. The atomic number of second impurity is $\frac{Z}{2}+1$

Answer 1

Answer: (A), (B)

$\frac{{\lambda }_0}{{\lambda }_1}=4\Rightarrow \frac{(Z_1-1{)}^2}{(Z-1{)}^2}=4\Rightarrow Z_1=2Z-1$

$\frac{{\lambda }_0}{{\lambda }_2}=\frac{1}{4}\Rightarrow \frac{(Z_2-1{)}^2}{(Z-1{)}^2}=\frac{1}{4}\Rightarrow Z_2=\frac{Z+1}{2}$

So, the answers are option (A) & (C).