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Question
The Kα and Kβ X-rays of molybdenum have wavelengths 0.71 A and 0.63 A respectively. Find the wavelength of Lα X-ray of molybdenum.
Solution
Given :
Wavelength of Kα X-rays, `lambda_1`= 0.71 A
Wavelength of Kβ X-rays, `lambda_2` = 0.63 A
For La X-ray of molybdenum,
a = 57
b = 1
From Moseley's equation,
`sqrt(v) = a(Z - b)`
Here, v = frequency of X-ray
Z = atomic number of the element
`sqrt(v) = a(Z - b)`
⇒ `sqrt(v) = a(57 - 1)`
= `a xx 56` ...(1)
For `Cu` (29),
`sqrt(1.88 xx 10^18) = a(29 - 1) = 28 a ...(2)`
Dividing (1) and (2)
`sqrt(v/(1.88 xx 10^18)) = (a xx 56)/(a xx 28) = 2`
⇒ `v = 1.88 xx 10^18 xx (2)^2`
= `4 xx 1.88 xx 10^18`
= `7.52 xx 10^18 "Hz"`
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