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 of Kα lines is λz for target A and λ1 and λ2 for two impurities. λzλ1=4andλzλ2=14 Assuming the screening constant of Kα lines to be unity, select the correct statement(s)
The atomic number of first impurity is 2z−1
The atomic number of first impurity is 2z+1
The atomic number of second impurity is (z+1)2
The atomic number of second impurity is z2+1
A
The atomic number of first impurity is 2z−1
B
The atomic number of second impurity is (z+1)2
C
The atomic number of second impurity is z2+1
D
The atomic number of first impurity is 2z+1
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Solution
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For Kα line, λ∝1(Z−1)2.
For first impurity, Let atomic number be Z1
So, (Z1−1)2(Z−1)2=4⇒Z1−1=2Z−2⇒Z1=2Z−1
For second impurity, Let atomic number be Z2
So, (Z1−1)2(Z−1)2=1/4⇒Z1−1=(Z−1)/2⇒Z1=(Z+1)/2
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