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 subsequently emitted. The emitted X-rays are analysed and the intensity is plotted against the wavelength figure. Assuming that only $K_{\alpha }$ intensities are detected, list the elements present in the sample from the plot. Use Moseley's equation

Answer 1

Given f = $(25\times {10}^{14}Hz)(Z-1{)}^2$

or, $\frac{c}{\lambda }=25\times {10}^{14}(Z-1{)}^2$

(a) $\frac{3\times {10}^8}{78.9\times {10}^{-12}\times 25\times {10}^{14}}=(Z-1{)}^2$

or $(Z-1{)}^2=0.001520\times {10}^6$ = 1520

$\Rightarrow$ Z-1 = 38.98

or Z = 39.98 = 40

i.e., It is (Zr).

(b) $\frac{3\times {10}^8}{146\times {10}^{-12}\times 25\times {10}^{14}}=(Z-1{)}^2$

or, $(Z-1{)}^2=0.00082219\times {10}^6$

or, Z-1 = 28.669

or, Z = 29.669= 30.

i.e., It is (Zn).

(c) $\frac{3\times {10}^8}{158\times {10}^{-12}\times 25\times {10}^4}=(Z-1{)}^2$

or, $(Z-1{)}^2=0.0007594\times {10}^4$

or, Z-1 = 27.5559

or, Z = 28.5589 =29.

i.e., It is (Cu).

(d) $\frac{3\times {10}^8}{198\times {10}^{-12}\times 25\times {10}^4}=(Z-1{)}^2$

or, $(Z-1{)}^2=0.000606\times {10}^4$

or, Z-1 = 24.6162

or, Z = 25.6162 = 26.

i,e., It is (Fe).