X – Rays
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X – Rays
Modern Physics of Class 12
X – RAYS
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When a heavy metal target is bombarded with high-energy (30 – 50keV) electrons, it emits X rays. The radiation involves both a continuous and a line spectrum, as shown in the fig.(16.6). The continuous spectrum, which starts at some minimum wavelength λo, arises from the rapid deceleration of the electrons when they enter the target – it is called bremsstrahlung, or braking radiation. The existence of minimum wavelength (or maximum frequency) is further evidence in favour of the photon concept. The highest frequency photon is emitted when an electron loses all its energy in one step. By equating the energy of the electron (eV) to the energy of the photon (hfo), we find hfo = eV or λo = hc/eV (16.17) |
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The minimum wavelength depends on the electron energy, but not on the target material.
The line spectrum depends on the element used as target. These characteristic X rays are produced when an electron knocks out an atomic electron from one of the inner levels. The ejected electron leaves a vacancy, which is then filled by an electron falling from a higher level. In the process a high – energy photon is emitted. If the transitions are to the n = 1 level, the X rays are labeled Kα, Kβ …….If they are to the n = 2 level, they are labeled Lα, Lβ, …
In 1913, Moseley noted that the characteristic lines shifted systematically as the target material was changed. He plotted the square root of the frequency of the Kα line versus the atomic number Z for many elements. The straight line he obtained is shown in the fig.(16.10).
Moseley’s plot did not pass through the origin. Let us see, why?. Once one of the two electrons in the n = 1 level is ejected, an electron in the next highest level will drop to the lower state to fill the vacancy and in the process it emits the Kα frequency. For this electron the electric field due to the nucleus is screened by the remaining electron in the n = 1 level. Moseley estimated that the effective nuclear charge for the Kα transition is (Z – 1)e. Thus Moseley’s law for the frequency of the Kα line is
= a(Z – 1) (16.18)
when a =
where R is the Rydberg constant c is the speed of light.
The wavelength of K – lines is given by
where n = 2, 3, 4,………… (16.19)
Example 16.8
Find the cut-off wavelength of the X-rays emitted by an X-ray tube operating at 30 kV.
Solution
For minimum wavelength, the total kinetic energy should be converted into an X-ray photon.
Thus,
λ = hv/E = 12400/E = 12400/30 x 10 3 = 0.41 Å
Example 16.9
Show that the frequency of Kβ X-ray of a material equals to the sum of frequencies of Kα and Lα X-rays of the same material.
Solution
The energy level diagram of an atom with one electron knocked out is shown above.
Energy of Kα X-ray is EKα = EL - EK
of Kβ X-ray is E kβ = EM - EK
and, of Lα X-ray is ELα = EM - EL
thus, E kβ = EKα + ELα
or
