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Question
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.
(Use Planck constant h = 6.63 × 10-34 Js= 4.14 × 10-15 eVs, speed of light c = 3 × 108 m/s.)
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Solution
Given:-
Wavelength of Kα X-ray, `lambda_1 = 21.3 "pm"`
Wavelength of Lα X-ray, `lambda_2 = 141 "pm"`
Energy of Kα X-ray (`E_1`) is given by
`E_1 = 1242/(21.3 xx 10^-3)`
= `58.309 xx 10^3 "eV"`
Energy of Lα X-ray (`E_2`) is given by
`E_2 = 1242/(141 xx 10^-5)`
= `8.8085 xx 10^3 "eV"`
Energy of Kβ X-ray (`E_3`) will be
`E_3 = E_1 + E_2`
`E_3 = (58.309 + 8.809) xx 10^3 "eV"`
`E_3 = 67.118 xx 10^3 "eV"`
Wavelength of Kβ X-ray (`lambda`) is given by
`lambda = (hc)/(E_3) = 1242/(67.118 xx 10^3)`
= `18.5 xx 10^-3 "nm" = 18.5 "pm"`
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