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Question: The X-ray wavelength of \(L_{\alpha}\) line of platinum (Z = 78) is \(1.30Å.\) The X –ray wavelength...

The X-ray wavelength of LαL_{\alpha} line of platinum (Z = 78) is 1.30A˚.1.30Å. The X –ray wavelength of LaL_{a} line of Molybdenum (Z = 42) is

A

5.41Å

B

4.20Å

C

2.70Å

D

1.35 Å

Answer

5.41Å

Explanation

Solution

The wave length of LαL_{\alpha} line is given by

1λ=R(z−7.4)2(122−132)⇒λ∝1(z−7.4)2⇒λ1λ2=(z2−7.4)2(z1−7.4)2⇒1.30λ2=(42−7.4)2(78−7.4)2\frac{1}{\lambda} = R(z - 7.4)^{2}\left( \frac{1}{2^{2}} - \frac{1}{3^{2}} \right) \Rightarrow \lambda \propto \frac{1}{(z - 7.4)^{2}} \Rightarrow \frac{\lambda_{1}}{\lambda_{2}} = \frac{(z_{2} - 7.4)^{2}}{(z_{1} - 7.4)^{2}} \Rightarrow \frac{1.30}{\lambda_{2}} = \frac{(42 - 7.4)^{2}}{(78 - 7.4)^{2}} ⇒\Rightarrow λ2=5.41A˚\lambda_{2} = 5.41Å.