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\mathrm{X} ray from a tube with a target \mathrm{A} of atomic number \mathrm{Z} shows strong \mathrm{K} lines for target \mathrm{A} and weak \mathrm{K} lines for impurities. The wavelength of \mathrm{K_\alpha} lines is \mathrm{\lambda_z} for target \mathrm{A \: and\: \lambda_1 \: and \: \lambda_2} for two impurities.

\mathrm{ \frac{\lambda_z}{\lambda_1}=4 \text { and } \frac{\lambda_z}{\lambda_2}=\frac{1}{4} . }

Screening constant of \mathrm{K}_\alpha lines to be unity. Select the correct statement(s)
 

Option: 1

The atomic number of first impurity is \mathrm{z-1}

 


Option: 2

The atomic number of first impurity is \mathrm{2 z+1.}
 


Option: 3

The atomic number of second impurity is \frac{(z+1)}{2}.
 


Option: 4

The atomic number of second impurity is \mathrm{\frac{Z}{2}+1.}


Answers (1)

best_answer

Mosley's law :
\mathrm{ \lambda \propto \frac{1}{(z-1)^2} }

\mathrm{ \frac{\lambda_z}{\lambda_1}=\frac{\left(z_1-1\right)^2}{(z-1)^2} }

\mathrm{z_1-1=(z-1) 2 }

\mathrm{ z_1=2 z-1 }

\mathrm{ \frac{\lambda_z}{\lambda_2}=\frac{1}{4}=\left(\frac{z_2-1}{z-1}\right)^2 }

\mathrm{ \Rightarrow \frac{z_2-1}{z-1}=\frac{1}{2} \Rightarrow 2 z_2-2=z-1 }

\mathrm{ z_2=\frac{z+1}{2}}







 

Posted by

Anam Khan

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