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 K_α 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.)

Answer 1

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).