An X- ray tube with a copper target is found to emit lines other those due to copper- The K- line of copper is known to have a wavelength 1-5405 A and the other two K- lines observed have wavelength 0-7092 A and 1-6578 A- Identify the impurities find the value of Z- atomic number-

According to Moseleys equation for K_α radiation 1 λ #160; =R( Z 1 ) #160; ^ 2 [ 1 1 ^ 2 1 2 ^ 2 #160; ] where λ = wavelength of ...

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Byju's Answer

Standard XII

Physics

Wien's Displacement Law

An X- ray t...

Question

An $X -$ ray tube with a copper target is found to emit lines other those due to copper. The $K_{α}$ line of copper is known to have a wavelength $1.5405 A$ and the other two $K_{α}$ lines observed have wavelength $0.7092 A$ and $1.6578 A$ . Identify the impurities (find the value of $Z$ , atomic number).

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Solution

According to Moseleys equation for $K_{α}$ radiation
$\frac{1}{λ} = R {(Z - 1)}^{2} [\frac{1}{1^{2}} - \frac{1}{2^{2}}]$ where $λ =$ wavelength of copper
Let $λ_{1}$ and $λ_{2}$ be the two other unknown wavelengths, then
$\frac{λ_{1}}{λ} = \frac{{(Z - 1)}^{2}}{{(Z_{1} - 1)}^{2}} = \frac{0.7092}{1.5405}$
Solving we get $Z_{1} = 42$
Similarly,
$\frac{λ_{2}}{λ} = \frac{{(28)}^{2}}{{(Z_{2} - 1)}^{2}} = \frac{1.6578}{1.5405}$
Solving, we get $Z_{2} = 28$

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An X− ray tube with a copper target is found to emit lines other those due to copper. The Kα line of copper is known to have a wavelength 1.5405 A and the other two Kα lines observed have wavelength 0.7092 A and 1.6578 A. Identify the impurities (find the value of Z, atomic number).

According to Moseleys equation for Kα radiation1λ=R(Z−1)2[112−122] where λ= wavelength of copperLet λ1 and λ2 be the two other unknown wavelengths, thenλ1λ=(Z−1)2(Z1−1)2=0.70921.5405Solving we get Z1=42Similarly,λ2λ=(28)2(Z2−1)2=1.65781.5405Solving, we get Z2=28