ELECTROMAGNETIC SPECTRUM

1. ELECTROMAGNETIC SPECTRUM

2. X-rays are electromagnetic radiations of very short wavelength ranging from 0.1 Å (0.01 nm) to 100 Å (10 nm). X-rays can be produced when kinetic energy of fast moving electrons is transformed into energy of electromagnetic waves.

3. There are FIVE important processes that may take place when the fast-moving electrons hit the anode and interact with the target atoms, (i) Scattering of electrons by the target, (ii)excitation of an outer orbital electron, (iii) ionization of an outer orbital electron, (iv) ionization followed by the emission of a characteristic X-rays (v) Continuous X-rays or bremsstrahlung ("braking radiation") production. The first two of these processes lead to the production of heat. In an X-ray tube 95% to 99% of the energy from decelerating electrons goes to heat via excitation and ionization of outer orbital electrons. The third and fourth of these processes lead to the production of X-ray photons. Between 1% and 5% goes to X-ray energy, mostly Bremsstrahlung.

5. Typical X-ray tubes

6. Production of X-rays X-rays are produced when electrons with high velocity (energy) interact with atoms. When high energetic electron beam incident on a solid target material, most of the energy of the electrons will be dissipated as heat and a very small amount of energy is emitted in the form of X-rays.

7. Production of X-rays continued • When high energetic electrons strike the target, X-rays are produced. • The wavelength of X-rays emitted will depend on various factors including, • the initial and final energy of the incident electron • nature of the target material • the nature of the interaction.

8. Hard X-rays and uses Hard X-rays:possessing higher penetration power (high applied voltage, lower wavelengths) – materials crystal structure analysis. (X-ray diffraction experiment, X-ray scattering experiment, X-ray absorption experiment etc.)

9. Some X-ray diffraction equipments for material analysis Debye-Scherrer camera attached X-ray machine Rigaku-Japan X-ray diffractometer Bruker-Germany

10. Soft X-rays and uses Soft X-rays: possessing lower penetration power (low applied voltage, higher wavelengths) – medical imaging. Diagnostic x-rays:  = 1 to 0.1 Å; Therapeutic:  = 0.1 to 104Å

11. Typical medical X-ray tube

12. INTENSITY AND FREQUENCY OF X-RAYS Intensity of X-rays:depends on the number of electrons striking the target per second  filament temperature  varies with filament current. The Frequency of X-rays:depends on the voltage between the anode (target) and cathode. Directly proportional to the applied voltage between the cathode and anode.

13. PROPERTIES OF X-RAYS • They are not charged particles • They affect photographic plates • They ionize the gas • They produce fluorescence in many substances • They are highly penetrating. Lead (Pb) is practically opaque to X-rays • They travel in straight lines with the velocity of light • They undergo reflection, refraction, interference, diffraction and polarization like light waves • They produce photoelectric effect and thereby exhibit corpuscular nature also.

14. X-ray spectra – radiation from X-ray tube

15. X-ray spectra – radiation from X-ray tube, continued • Based on the characteristics & the origin of X-rays, X-ray spectra may be classified as, • Continuous X-ray spectrum[bremsstrahlung]: a background of continuous radiation. • Characteristic X-ray spectrum:the superimposed lines on the continuous background, characteristic of the material of the target, that occurs only when the applied voltage is greater than a particular value.

16. Origin of – Continuous X-ray spectrum – bremsstrahlung – “braking” radiations Result of Interaction (collision) between high speed electron and nucleus. As the electron moves past the nucleus of an atom, it slows down or brakes.Electron is deflected and loses part of its energy, which is emitted as radiation. Each electron may have one or more bremsstrahlung interactions resulting in loss of part or all its energy, therefore photon may have any energy up to initial electron energy.

18. "Bremsstrahlung" means "braking radiation" and is retained from the original German to describe the radiation which is emitted when electrons are decelerated or "braked" when they are fired at a metal target. Accelerated charges give off electromagnetic radiation, and when the energy of the bombarding electrons is high enough, that radiation is in the X-ray region of the electromagnetic spectrum. It is characterized by a continuous distribution of radiation which becomes more intense and shifts toward higher frequencies when the energy of the bombarding electrons is increased. The bombarding electrons can also eject electrons from the inner shells of the atoms of the metal target, and the quick filling of those vacancies by electrons dropping down from higher levels gives rise to sharply defined Characteristic X-rays.

20. Let be the initial energy of the electron and Let be the final energy of the electron after the interaction with target atom. Then the energy of the photon emitted is given by The short wavelength limit corresponds to the case when the electron loses all its kinetic energy.

21. Since the kinetic energy of the electron is acquired due to the application of an electric potential V, we have, Comparing Eqs. (2) and (3) we get, ( is in angstroms & V is in volts) Equation (4) is known as Duane-Hunt law (limit) and this equation can be used for the experimental determination of Planck’s constant.

22. Properties of continuous X-ray spectrum • Continuous X-ray spectrum is that portion of the spectrum in which the intensity of X rays varies continuously & smoothly over a wide range of wavelength. • For each applied voltage that accelerates the impinging electrons, there is a certain minimum cut off wavelength called the Duane-Hunt limit. Below this cut off wavelength no X ray is emitted. • The minimum cut off wavelength is independent of the target element but is dependent on the applied voltage. • The cut off wavelength decreases with the increasing applied voltage & shifts towards the shorter wavelength. • The maximum intensity peak increases with the increasing applied voltage & shifts towards the shorter wavelength region.

23. ORIGIN OF CHARACTERISTIC X-RAY SPECTRUM

26. Electron transitions to lower atomic levels in heavy atoms have quantum energies which place them in the X-ray region of the electromagnetic spectrum. The x-ray emissions associated with these transitions are called characteristic X-rays.

27. During the transition of electron from outer shell to inner shell the energy difference appears as X-ray photon of frequency A K series of lines results from the transition of electron from the higher shell to K shell. Example: L  K transition  K M K transition  K M  L transition  L N L transition  L

29. Summary of continuous and characteristic X-rays

30. MOSELEY’S LAW

31. “The frequency of the characteristic x-rays emitted by different target elements varies directly as the square of the effective atomic number of the elements.” Mathematically, Moseley’s law may be stated as  = a2(Z – b)2   = a(Z – b) where, is the frequency of the x-ray emitted, Z is the atomic number of the element. b is called the screening constant whose value is different for different series of the x-ray spectrum.For K series, b=1; for L series, b=7.4. (Z-b) is called the effective atomic number.

32.  = a(Z – b)

33.  = a(Z – b) The above relation can be obtained by considering Bohr’s theory with modification for the screening effect of electrons as follows. From Bohr’s theory of hydrogen atom, the energy of the electron in the nth shell is given by, R = Rydberg constant = 1.1  107/m c = speed of light in vacuum = 3  108 m/s h = Planck’s constant = 6.62  1034J.s n = principal quantum number, n = 1, 2, 3,…..

34. For hydrogen atom, For hydrogen atom, only one electron moves in the field of positive nucleus, but for the other atoms, the electron is under the action of two fields – nucleus and other electrons. Hence the nucleus is screened by electrons surrounding it. This effect can be involved in the above equation by replacing Z by (Z – ), where  represents the nuclear screening constant. Hence the energy corresponding to the transition of electron from level to level is,

35. The electrons in the K shell of an atom of an element with atomic number Z will experience the influence of the entire nuclear charge Ze. But for an electron in a L shell, the two 1S electrons in the K shell screen the positive charge on the nucleus & the effective charge experienced by the electron in the L shell is therefore (Z – 2)e & not Ze.

36. When an impinging electron removes an electron from the K shell, the electron in the L shell will see only (Z-1)e as the effective charge on the nucleus. This is due to the screening effect of the one K electron. So, for the K X ray, the screening constant is 1 & the Zeff is (Z – 1).

37. Therefore for K line

38. Similarly for L line,

39. Applications of Moseley’s Law • Periodic table was previously an arbitrary scheme of classification of elements. Moseley’s law gave a strong link between the periodic table & the atomic theory. It provided a systematic way of arranging the elements in the periodic table with atomic number as the basis. • It removed the discrepancies in the arrangement of certain elements such as, • Argon (Z=18, A=40) & Potassium (Z=19, A=39) • Cobalt (Z=27, A=58.9) & Nickel (Z=28, A=58.7) • Tellurium (Z=52, A=127.6)&Iodine (Z=53, A=126.9) • By assigning proper places in the periodic table.

40. 3.It provided a simple, direct & powerful method of determining the atomic number of elements. • It predicted & hence led to the discovery of many new elements for which gaps were provided in the periodic table. Elements such as technetium (z=43), cerium (z=58), hafnium (z=72), Promethium (z=61) etc were discovered this way. • It ruled out the possibility of any new element which would occupy the periodic table in between the existing elements.

41. The potential difference across an X-ray tube is 50kV and the current through it is 2.5 mA. Calculate (a) the number of electrons striking the anode per second, (b) the speed with which they strike it and (c) the approximate rate of production of heat in the anode. (a) One ampere current is a flow of charge of one coulomb per second. Thus 2.5 mA is equivalent to, (b) (c)

42. Which element (what is the atomic number? Identify the element) has a K X-ray line whose wavelength is 0.180 nm? Given: Rydberg constant R= 1.1  107/m (Cobalt)

43. When electrons bombard a molybdenum target, they produce both continuous and characteristic X-rays. If the accelerating potential is 50 keV, determine (a)min(b) the wavelength of K line and (c) the wavelength of the K line. Given: Atomic number of molybdenum = 42; Rydberg constant = 1.1  107m1.

45. In a characteristic x-ray spectrum of Co, the wavelengths of Kline are 178.9pm for cobalt and 143.5pm for a second faint line due to impurity. What is the impurity element?

46. HRK-Sample Problem 48-1: Calculate the cutoff wavelength for the continuous spectrum of x-rays emitted when 35-keV electrons fall on a molybdenum target. Solution:

47. HRK-Exercise 48.1: Show that the short-wavelength cutoff in the continuous x-ray spectrum is given by where ΔV is the applied potential difference in kilovolts. Solution:The highest energy x-ray photon will have an energy equal to the bombarding electrons,

48. HRK-Exercise 48.9: X-rays are produced in an x-ray tube by a target potential of 50.0 keV. If an electron makes three collisions in the target before coming to rest and loses one-half of its remaining kinetic energy on each of the first two collisions, determine the wavelengths of the resulting photons. Neglect the recoil of the heavy target atoms. Solution

50. HRK-Exercise 48.12: The binding energies of K-shell and L-shell electrons in copper are 8.979 keV and 0.951 keV, respectively. If a K x-ray from copper is incident on a sodium chloride crystal and gives a first-order Bragg reflection at 15.9 when reflected from the alternating planes of the sodium atoms, what is the spacing between these planes ? Solution: