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Question
Continuous X-rays are made to strike a tissue paper soaked with polluted water. The incoming X-rays excite the atoms of the sample by knocking out the electrons from the inner shells. Characteristic X-rays are analysed and the intensity is plotted against the wavelength. Assuming that only Kα intensities are detected, list the elements present in the sample from the plot. Use Moseley's equation v − (25 × 1014Hz)(Z − 1)2.
(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 :-
`f = (25 × 10^14 "Hz") (Z − 1)^2`
`or c/lambda = 25 xx 10^14(Z - 1)^2`
(a) `(3 xx 10^8)/(78.9 xx 10^-12 xx 25 xx 10^14)` = `(Z - 1)^2`
or `(Z - 1)^2 = 0.001520 xx 10^6 = 1520`
`⇒ Z - 1 = 38.98`
`or Z = 39.98 = 40`
Thus , it is (Zr) .
(b) `(3 xx 10^8)/(146 xx 10^-12 xx 25 xx 10^14)` = `(Z - 1)^2`
`or (Z - 1)^2 = 0.00082219 xx 10^6`
`or Z - 1 = 28.669`
`or Z = 29.669 = 30`
Thus , it is (Zn).
(c) `(3 xx 10^8)/(158 xx 10^-12 xx 25 xx 10^14) = (Z - 1)^2`
`or (Z -1)^2 = 0.0007594 xx 10^4`
`or Z - 1 = 27.5559`
`or Z - 1 = 28.5589 = 29`
Thus , it is (Cu).
(d) `(3 xx 10^8)/(198 xx 10^-12 xx 25 xx 10^14) = (Z - 1)^2`
`or (Z - 1)^2 = 0.000606 xx 10^4`
`or Z-1 = 24.6162`
`or Z = 25.6162 = 26`
Thus , it is (Fe).
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