CALCULATION OF XRAY WAVELENGTHS IF ELECTRONS ARE ACCELERATED TO

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X ray wavelengths

Calculation of X-ray wavelengths

If electrons are accelerated to a velocity v by a potential difference V and then allowed to collide with a metal target, the maximum frequency [of the X-rays emitted is given by the equation:

½ mv²= eV = hf

X ray frequency (f) = eV/h

Therefore:

Example

Calculate the minimum wavelength of X-rays emitted when electrons accelerated through 30 kV strike a target.

f = [1.6 x 10^-19 x 3 x 10⁴]/ 6.63 x 10^-34 = 7.2x10¹⁸ Hz

Therefore the wavelength  (= c/f) is 0.41 x 10^-10 m = 0.04 1 nm (compared with some 600 nm for yellow light).

his shows that the maximum frequency is directly proportional to the accelerating voltage.

Moseley’s law

In 1914 Moseley proposed a law showing how the X-ray frequency can be related to the proton (atomic) number Z of the target material. If f is the X-ray frequency, then:

X ray frequency (f) = k(Z- b)²

where k and b are constants, k having a value of 2.48 x 10¹⁵.

Plotting a graph of Z against √f will give a straight line as shown in the diagram, and in fact Moseley predicted the existence of elements 43, 61, 72 and 75 by the gaps that he found in his original version of the graph.

CALCULATION OF XRAY WAVELENGTHS IF ELECTRONS ARE ACCELERATED TO

Electrons falling to the lowest level (or K-shell) in the atom from other excited levels give out X-rays in a series of wavelengths like an optical spectrum. This is known as the K-series, and individual lines are denoted by K_, K_ and so on. Electron transitions ending on the second level are known as the L-series.

The following table shows the wavelengths of the K_, lines for some elements:

Element	Proton number	Wavelength (nm)	Element	Proton number	Wavelength (nm)
Aluminium	13	0.823	Copper	29	0.139
Calcium	20	0.335	Bromine	35	0.104
Manganese	25	0.210	Silver	47	0.056
Iron	26	0.194	Tungsten	74	0.021
Cobalt	27	0.179	Uranium	92	0.017
Nickel	28	0.166

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