Modern Physics X - Ray

MODERN PHYSICS What are X - Rays X-rays are electromagnetic radiation of very short wavelength 0.1 Å and 100 Å) and high energy which are emitted when fast moving electrons or cathode rays strike a target of high atomic mass. The X-Rays extends from the ultraviolet band to gamma rays band. Although their is very thin line between the Xray and gamma rays but they are distinguished by the source of their generation. In the older days the X-Rays were distinguished from gamma rays by the wavelength and frequency but with time it has been observed that their exists X-Rays and gamma rays overlapping band and hence it is then understood that the distinction between them is source of generation. Historical background On Nov. 1895, Wilhelm Conrad Rontgen (accidentally) discovered an image cast from his cathode ray generator, projected far beyond the possible range of the cathode rays (now known as an electron beam). Further investigation showed that the rays were generated at the point of contact of the cathode ray beam on the interior of the vacuum tube, that they were not deflected by magnetic fields, and they penetrated many kinds of matter. Rontgen named the new form of radiation X-radiation (X standing for “Unknown”). COOLIDGE METHOD Coolidge developed thermoionic vacuum X–ray tube in which electron are produced by thermoionic emission method. Due to high potential difference electrons (emitted due to thermoionic method) move towards the target and strike from the atom of target due to which X–ray are produced. Experimentally it is observed that only 1% or 2% kinetic energy of electron beam is used to produce X–ray. Rest of energy is wasted in form of heat. Characteristics of Target (a) Must have high atomic number to produce hard X–rays. (b) High melting point to withstand high temperature produced. (c) High thermal conductivity to remove the heat produced (d) Tantalum, platinum, molybdenum and tungsten serve as target materials Control of intensity : The intensity of X–ray depends on number of electrons striking the target and number of electron depend on temperature of filament which can be controlled by filament current. Thus intensity of X–ray depends on current flowing through filament. Control of Penetrating Power: The Penetrating power of X–ray depends on the energy of incident electron. The energy of electron can be controlled by applied potential difference. Thus penetrating power of X–ray depend on applied potential difference. Thus the intensity of X–ray depends on current flowing through filament while penetrating power depends on applied potential difference Soft X–ray Hard X–ray Wavelength 10 Å to 100 Å 0.1 Å – 10 Å Energy 1 24 00 eV–Å  1 24 00 eV–Å  Penetrating power Less More Use Radio photography Radio therapy Continuous spectrum of X–ray : When high speed electron collides from the atom of target and passes close to the nucleus. There is coulomb attractive force due to this electron is deaccelerated i.e. energy is decreased. The loss of energy during deacceleration is emitted in the form of X–rays. X–ray produced in this way are called Braking or Bremstralung radiation and form continuous spectrum. In continuous spectrum of X–ray all the wavelength of X–ray are present but below a minimum value of wavelength there is no X–ray. It is called cut off or threshold or minimum wavelength of X–ray. The minimum wavelength depends on applied potential. Loss in Kinetic Energy 1 1 mv12 – mv22 = h+ heat energy if v2 = 0 , v1 = v (In first collision, heat = 0) 2 2 1 mv2 = hmax 2 ...(i) 1 mv2 = eV 2 ...(ii) [here V is applied potential] from (i) and (ii) hmax = eV  1 24 00 1 24 00 hc = eV min = × volt = × 10–10 m × volt V V  min Continuous X–rays also known as white X–ray. Minimum wavelength of these spectrum only depends on applied potential and doesn' t depend on atomic number. Characteristic Spectrum of X–ray When the target of X–ray tube is collide by energetic electron it emits two type of X–ray radiation. One of them has a continuous spectrum whose wavelength depend on applied potential while other consists of spectral lines whose wavelength depend on nature of target. The radiation forming the line spectrum is called characteristic X–rays. When highly accelerated electron strikes with the atom of target then it knockout the electron of orbit, due to this a vacancy is created. To fill this vacancy electron jumps from higher energy level and electromagnetic radiation are emitted which form characteristic spectrum of X–ray. Whose wavelength depends on nature of target and not on applied potential. MODERN PHYSICS From Bohr Model n1 = 1, n2 = 2, 3, 4.......K series n1 = 2, n2 = 3, 4, 5.......L series n1 = 3, n2 = 4, 5, 6.......M series First line of series =  Second line of series =  Third line of series =  Transition Wave– length L  K K (2 1) MK Energy hK = hK K (3 1) ML hK = hK L (3 2) Energy Wavelength difference hL = hL –(EK–EL) K = = 1 2 40 0 eVÅ (E K  E L ) –(EK–EM) K= = hc (EK  EL ) hc (E K  E M ) 1 24 00 eVÅ (E K  E M ) –(EL–EM) L = = hc (E L  E M ) 12 40 0 eVÅ (E L  E M ) MOSELEY'S LAW Moseley studied the characteristic spectrum of number of many elements and observed that the square root of the frequency of a K– line is closely proportional to atomic number of the element. This is called Moseley's law.  (Z – b)   (Z – b)2 = a (Z – b)2 Z = atomic number of target  = frequency of characteristic spectrum b = screening constant (for K– series b=1, L series b=7.4) a = proportionality constant From Bohr Model Comparing (i) and (ii) 1 1  = RcZ2  2  2   n1 n 2  1 1  a = Rc  2  2   n1 n 2  ...(i) ...(ii) Z  Thus proportionality constant 'a' does not depend on the nature of target but depend on transition. Bohr model  Moseley's correction 1. For single electron species 1. For many electron species 2. 1 1  E = 13.6Z2  2  2  eV  n1 n 2  2. 1 1  E = 13.6 (Z–1)2  2  2  eV  n1 n 2  3. 1 1   = RcZ2  2  2  n n  1 2  3. 1 1   = Rc(Z–1)2  2  2   n1 n 2  4. 1 1  1 = RZ2  2  2    n1 n 2  4. 1 1  1 = R (Z – 1)2  2  2    n1 n 2  For X–ray production, Moseley formulae are used because heavy metal are used. When target is same   1 1 1  2 2 n1 n 2 When transition is same   1 (Z  b)2 ABSORPTION OF X–RAY When X–ray passes through x thickness then its intensity I = I 0e–x I0 = Intensity of incident X–ray I = Intensity of X–ray after passing through x distance  = absorption coefficient of material I0  Intensity of X–ray decrease exponentially.  Maximum absorption of X–ray  Lead  Minimum absorption of X–ray  Air I x HALF THICKNESS (x1/2) The distance travelled by X–ray when intensity become half the original value x1/2 = l n2  Ex. When X–rays of wavelength 0.5Å pass through 10 mm thick Al sheet then their intensity is reduced to one sixth. Find the absorption coefficient for Aluminium . Sol.  2 .3 03 x 2 .30 3 2.30 3  0 .77 8 1 I  log  o   log10 6   0.1 7 52 / mm  I 10 10 MODERN PHYSICS DIFFRACTION OF X–RAY Diffraction of X–ray is possible by crystals because the interatomic spacing in a crystal lattice is order of wavelength of X–rays it was first verified by Lauve. Diffraction of X–ray take place according to Bragg's law 2d sin = n d = spacing of crystal plane or lattice constant or distance between adjacent atomic plane  = Bragg's angle or glancing angle  = Diffracting angle n = 1, 2, 3 ....... For Maximum Wavelength sin  = 1, n = 1  max = 2d so if  > 2d diffraction is not possible i.e. solution of Bragg's equation is not possible. PROPERTIES OF X–RAY (i) X–ray always travel with the velocity of light in straight line because X–rays are em waves (ii) X–ray is electromagnetic radiation it show particle and wave both nature (iii) In reflection, diffraction, interference, refraction X–ray shows wave nature while in photoelectric effect it shows particle nature. (iv) There is no charge on X–ray thus these are not deflected by electric field and magnetic field. (v) X–ray are invisible. (vi) X–ray affects the photographic plate (vii) When X–ray incidents on the surface of substance it exerts force and pressure and transfer energy and momentum (viii) Characteristic X–ray can not obtained from hydrogen because the difference of energy level in hydrogen is very small. Ex. Show that the frequency of K X–ray of a material is equal to the sum of frequencies of K and L X–rays of the same material. Sol. The energy level diagram of an atom with one electron knocked out is shown above. Energy of K X–ray is EK =EL – EK and of K X–ray is EK = EM – EK and of L X–rays is EL = EM – EL thus EK = EK + EL or K = K + L Ex. Find in Z1 and Z2 which one is greater.  1 1 cR  2  2  . (Z – b) n   1 n2  If Z is greater then  will be greater,  will be less  1 < 2  Z1 > Z2. Sol.  Ex. A cobalt target is bombarded with electrons and the wavelength of its characteristic spectrum are measured. A second, fainter, characteristic spectrum is also found because of an impurity in the target. The wavelength of the K  lines are 178.9 pm (cobalt) and 143.5 pm (impurity). What is the impurity? Using Moseley’s law and putting c/ for  (and assuming b = 1), we obtain Sol.   c  aZ c 0  a c0 c0 Dividing yields x Substituting gives us  c  aZ x  a x and Zx  1 Zc0  1 178 .9 pm Zx  1 = . 143 .5 pm 27  1 Solving for the unknown, we find Zx = 30.0; the impurity is zinc. Ex. Sol. Find the constants a and b in Moseley’s equation v  a( Z  b) from the following data. Element Z Wavelength of K X-ray Mo Co 42 27 71 pm 178.5 pm Moseley’s equation is v  a( Z  b) Thus, c  a( Z1  b) 1 From (i) and (ii) = (3  10 8 m / s)1/ 2 42  27 ....(i) and  1 1  c   a ( Z1  Z 2 )    2   1 c  a( Z 2  b) 2 or,, ....(ii)  1 c 1    a = (Z  Z )   2  1 2  1   1 1 7 1/2   12 1/ 2 12 1 / 2  = 5.0 × 10 (Hz) (178.5  10 m)   (71 10 m) Dividing (i) by (ii), 2 Z b  1 1 Z2  b or, 178 .5 42  b  71 27  b or, b = 1.37