Characteristic And Continuous X-rays - Concepts Of Physics
Characteristic and Continuous X-raysJitender Singh www.concepts-of-physics.comOctober 18, 20191IntroductionHV The x-rays are produced in a Coolidge tube when a high energyelectron interacts with a heavy metal target.The high energy electrons get decelerated by Coulomb’s interaction with the target atom. These decelerating electrons emit continuous X-rays (or bremsstrahlung). When an electron loses its entire energy in a single Coulomb’s interaction then X-rays of minimumwavelength (cut-off wavelength) are emitted.The cut-off wavelength of the continuous X-ray spectrum is relatedto the accelerating potential V of the Coolidge tube byλcut off LVCathodeSolved Problems on X-raysProblem from IIT JEE 2008e Anode X-rayFigure 1: In Coolidge Tube, the intensityof x-rays is controlled by the filamentcurrent/voltage (LV) and the frequencyof x-rays is controlled by the accelerating voltage (HV).hc12400 (Å/V).eVVTypically, accelerating voltage is a few thousand Volts and cut offwavelength is of the order of an Angstrom. The cut-off frequencyof continuous x-rays is given by νcut off c/λcut off . The cutoff wavelength decreases when the accelerating potential of Coolidge tube isincreased. The intensity of X-rays increases with an increase in accelerating potential as shown in the figure. The intensity of X-raysdepends on multiple factors.The high energy electrons also knock out an inner shell electron ofthe target atom. The characteristic X-rays are emitted when an electron(in atom) makes a transition from a high energy state to a low energystate to fill the vacancy. For example, in Kα X-ray series, the electronsmakes transition from the high energy state to the K shell of the atom.The frequency of characteristic X-rays is related to the atomic number of the target element by Moseley?s Law ν a( Z b). The frequencyof characteristic X-rays depends on the target material (it is independent of the accelerating potential).2 Target Nucleus e e X-rayFigure 2: An electron decelerated byCoulomb’s interaction of target atomemits X-rays in the continuous spectrum.Relative IntensityKα1.050 kV25 kVLαKαLα0.50.250.51.01.52.0Wavelength (Å)Figure 3: The spectrum shows the variation of X-rays intensity with wavelength.It consists of bremsstrahlung (continuous spectrum) and peaks (characteristicspectrum). Note the variation of cut-offwavelength with accelerating potential.Which of the following statements is em wrong /em in the contextof X-rays generated from a X-ray tube?LβKβKαLαN n 4M n 3L n 2K n 1Figure 4: The characteristic X-rays areemitted when an electron in a high energy state makes a transition to a lowenergy state.
x-rays copyright 2019 by jitender singh www.concepts-of-physics.com(A) Wavelength of characteristic X-rays decreases when the atomicnumber of the target increases.(B) Cut-off wavelength of the continuous X-rays depends on the atomicnumber of the target.(C) Intensity of the characteristic X-rays depends on the electrical powergiven to the X-ray tube.(D) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube.Solution: The frequency ν of characteristic X-rays is related to atomicnumber Z by Moseley’s law, ν a ( Z b ).(1)which gives,λ cc. 2νa ( Z b )2(2)Thus, wavelength decreases with an increase in Z. The cut-off wavelength of continuous X-rays corresponds to the maximum energy ofan electron in X-ray tube. It is given by,hc/λ eV,(3)where V is accelerating potential. The intensity of X-rays depends onthe number of electrons striking the target per second, which in turndepends on electrical power given to the X-ray tube as energy of eachelectron is eV.Problem from IIT JEE 2000Electrons with energy 80 keV are incident on the tungsten target of anX-ray tube. K-shell electrons of tungsten have 72.5 keV energy. X-raysemitted by the tube contains only,(A) a continuous X-ray spectrum (Bremsstrahlung) with a minimumwavelength of 0.155 Angstrom.(B) a continuous X-ray spectrum with all wavelengths.(C) the characteristic X-ray spectrum of tungsten.(D) a continuous X-ray spectrum with a minimum wavelength of 0.155 Angstrom and the characteristic X-ray spectrum of tungsten.Solution: The energy of incident electron (Ein 80 keV) is sufficientto knock out K-shell electrons (72.5 keV) thereby emitting characteristic X-rays. The minimum wavelength of continuous spectrum corresponds to Ein and is given byλ hc(6.63 10 34 ) (3 108 ) 0.155 Angstrom.Ein(80 103 ) (1.602 10 19 )2
x-rays copyright 2019 by jitender singh www.concepts-of-physics.com3Problem from IIT JEE 1988The potential difference applied to an X-ray tube is increased. As aresult, in the emitted radiation,(A) the intensity increases.(B) the minimum wavelength increases.(C) the intensity remains unchanged.(D) the minimum wavelength decreases.Solution: The minimum wavelength of X-ray is related to the appliedpotential byλmin hc12420 Angstrom.eVVThus, the minimum wavelength decreases when V is increased. Theintensity is the rate of energy flow per unit area. The energy of photonsincreases when V is increased. Thus, intensity also increases with anincrease in the applied potential.However, intensity of X-rays is generally controlled by the filamentcurrent. An increase in the filament current increases its temperature which in turn increases the rate of electron emissions (thermionicemissions). Thus, more number of electrons strikes the target leadingto increase in number of X-ray photons.Problem from IIT JEE 2008Which of the following statements is wrong in the context of X-raysgenerated from a X-ray tube?(A) Wavelength of characteristic X-rays decreases when the atomicnumber of the target increases.(B) Cut-off wavelength of the continuous X-rays depends on the atomicnumber of the target.(C) Intensity of the characteristic X-rays depends on the electrical powergiven to the X-ray tube.(D) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube.Solution: The frequency ν of characteristic X-rays is related to atomicnumber Z by Moseley’s law, ν a ( Z b ),which givesλ cc 2.νa ( Z b )2Click to see our book: 100Solved Problems on Units,Dimensions and MeasurementsClick to see our book: 100Solved Problems on Rectilinear Motion
x-rays copyright 2019 by jitender singh www.concepts-of-physics.com4Thus, the wavelength of emitted X-rays decreases with increase in Z.The cut-off wavelength of continuous X-rays corresponds to maximumenergy of electron in X-ray tube. It is given byhc/λ eV,where V is the accelerating potential. The intensity of X-rays dependson the number of electrons striking the target per second, which, inturn, depends on the electrical power given to the X-ray tube as energyof each electron is eV.3Questions on X-raysQuestion 1Question 1 (IIT JEE 1998): /b X-rays are produced in an X-ray tubeoperating at a given accelerating voltage. The wavelength of the continuous X-rays has values from(A) 0 to .(B) λmin to , where λmin 0.(C) 0 to λmax , where λmax .(D) λmin to λmax where 0 λmin λmax .Answer: (B) The wavelength in continuous X-ray spectrum has a lowerlimit given by hc/eV. There is no upper limit on wavelength.Question 2The shortest wavelength of X-ray emitted from an X-ray tube dependson(A) the current in the tube.(B) the voltage applied to the tube.(C) the nature of the gas in tube.(D) the atomic number of the target material.Answer: (B) The shortest wavelength of X-ray emitted by X-ray tubedepends on the applied voltage V.Question 3When the number of electrons striking the anode of an X-ray tubeis increased the . . . . . . . . . of the emitted X-rays increases while whenthe speeds of the electrons striking the anode are increased the cut-offwavelength of the emitted X-rays . . . . . . . . . .Click to see our book: 100Solved Problems on Motionin a PlaneClick to see our book: 300Solved Problems on Rotational MechanicsClick to see our book: IIT JEEPapers
x-rays copyright 2019 by jitender singh www.concepts-of-physics.com(A) cut off wavelength, decreases(B) cut-off wavelength, decreases(C) intensity, increases(D) intensity, decreasesAnswer: (D) The intensity of X-ray increases when the number ofelectrons striking the anode increases. The cut-off voltage decreaseswhen the energy (speed) of the electrons striking the anode increases.Question 4Consider a photon of a continuous X-ray coming from a Coolidge tube.Its energy comes from(A) the kinetic energy of the striking electron(B) the kinetic energy of the free electrons of the target(C) the kinetic energy of the ions of the target(D) an atomic transition in the targetAnswer: (A) The kinetic energy of the striking electron. For characteristic X-rays, the answer is D.References[1] IIT JEE Physics by Jitender Singh and Shraddhesh Chaturvedi[2] Concepts of Physics Part 2 by HC Verma (Link to Amazon)[3] Characteristic and Continuous X-rays, Hyperphysics[4] Article on Coolidge Tube, Oak Ridge[5] Properties of X-rays (pdf), Stanford[6] Features of X-rays spectrum, Miniphysics5
Click to see our book: 100 Solved Problems on Motion in a Plane Click to see our book: 300 Solved Problems on Rota-tional Mechanics Click to see our book: IIT JEE Papers Question 1 Question 1 (IIT JEE 1998): /b X-rays are produced in an X-ray tube operating at a given accelerating voltage. The wavelength of the con-tinuous X-rays has values .
Sherwood Scientific Near infrared 3000 - 780 Visible rays 780 - 380 Near ultra violet rays(UV) 380 - 200 Far ultra violet rays 200 - 50 X-rays 50 - 10-1 (Gamma) X-rays 10-1 – 10-3 Cosmic rays 10-3 and less Most of us are more familiar with the vis
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Wood Rays After you examine the pores, look at the rays. Wood rays look like small stripes that go from one edge of a piece of wood to the other edge on the cross-sectional face. Wood rays transport food and water horizontally in the tree. The rays in most species are unique and allow for easy identification. Oaks, for example, have very large .
Advanced Physics Laboratory X-ray Spectroscopy 1. Introduction X-rays are KeV photons. Atomic X-rays are emitted during electronic transitions to the inner shell states in atoms of modest atomic number. These X-rays have characteristic energies related to the atomic number, and each element therefore has a characteristic X-ray spectrum.
Sep 15, 2020 · Topic: Segments, rays, and distance Aim : What are . will be able to describe what is a line segment and a ray. HW# 002: Page 5 of this lesson plan Do Now: What are some real-life examples of a ray . How can we name a ray? Name 3 rays pictured below. Definition: Opposite rays are two
Primary Cosmic Rays Flux of stable ( 106 yrs) charged particles and nuclei Primary Cosmic Rays: accelerated at astrophysical sources Protons 87% He 12% 1% heavier nuclei: C, O, Fe and other ionized nuclei synthesized in stars 2% electrons γ-rays, neutrinos There may be primary components of anti-p and e (antimatter in the Universe?) But composition varies with energy (bulk of CR is at 1 GeV).
beam) can be interpreted as a projection of two skew rays with α 0 and α π/2 in Eq. (1) onto the x-z plane. It is worth noting that any two skew rays with α differing by π/2 may be used as the launched rays, and all of Herloski's results will still be valid. The choice of rays to launch is not limited to the waist ray and divergence ray .
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