The wavelengths of $K_{α}$ and $L_{α}$ X-rays of a material are 21.3 pm and 141 pm respectively. Find the wavelength of $K_{β}$ X-ray of the material.

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Solution

Given $E_{1} = \frac{1242}{21.3 \times 10^{- 3}}$

= 58.309 $\times 10^{3}$ eV

$E_{2} = \frac{1242}{141 \times 10^{- 5}}$

= $8.8085 \times 10^{3}$ eV

E=3 = $E_{1} + E_{2}$

= (58.309+8.909) 10 eV

= 67.118 $\times 10^{3}$ eV

$λ = \frac{h c}{E^{3}} = \frac{1242}{67.118 \times 10^{3}}$

= 18.5 $\times 10^{- 3}$ nm = 18.5 pm.

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The wavelengths of Kα and Lα X-rays of a material are 21.3 pm and 141 pm respectively. Find the wavelength of Kβ X-ray of the material.

Given E1=124221.3×10−3 = 58.309 ×103 eV E2=1242141×10−5 = 8.8085×103 eV E=3 = E1+E2 = (58.309+8.909) 10 eV = 67.118 ×103 eV λ=hcE3=124267.118×103 = 18.5 ×10−3 nm = 18.5 pm.

The wavelengths of $K_{α}$ and $L_{α}$ X-rays of a material are 21.3 pm and 141 pm respectively. Find the wavelength of $K_{β}$ X-ray of the material.