matriculation physics ( x-rays )

1

PHYSICS CHAPTER 12

is defined as an electromagnetic an electromagnetic radiation of shorter wavelength radiation of shorter wavelength than UV radiation produced by than UV radiation produced by the bombardment of atoms by the bombardment of atoms by high energy electrons in x-ray high energy electrons in x-ray

tubetube.

CHAPTER 12: X-raysCHAPTER 12: X-rays(2 Hours)(2 Hours)

discovered by Wilhelm Konrad Rontgen Wilhelm Konrad Rontgen

in 1895.

PHYSICS CHAPTER 12

2

At the end of this chapter, students should be able to: At the end of this chapter, students should be able to: Explain Explain with the aid of a diagram, the production of with the aid of a diagram, the production of

X-rays from an X-ray tube. X-rays from an X-ray tube. ExplainExplain the production of continuous and characteristic the production of continuous and characteristic

X-ray spectra.X-ray spectra. Derive and use Derive and use the formulae for minimum wavelength for the formulae for minimum wavelength for

continuous X-ray spectra, continuous X-ray spectra,

IdentifyIdentify the effects of the variation of current, the effects of the variation of current, accelerating voltage and atomic number of the anode on accelerating voltage and atomic number of the anode on the continuous and characteristic X-ray spectra.the continuous and characteristic X-ray spectra.

Learning Outcome:

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12.1 X-ray spectra (1 hour)

eV

hcmin

PHYSICS CHAPTER 12

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12.1.1 Properties of x-rays Its properties are

x-rays travel in a straight linesstraight lines at the speed of lightspeed of light. x-rays cannot cannot be deflecteddeflected by electricelectric or magnetic fieldsmagnetic fields.

(This is convincing evidence that they are uncharged or neutral particlesneutral particles)

x-rays can be diffracteddiffracted by the crystal latticecrystal lattice if the spacing between two consecutive planes of atoms approximately equal to its wavelength.

x-rays affect photographic filmaffect photographic film. x-rays can produce fluorescencefluorescence and photoelectric photoelectric

emissionemission. x-rays penetrate matterpenetrate matter. Penetration power is leastleast in the

materials of high densitymaterials of high density.

12.1 X-ray spectra

PHYSICS CHAPTER 12

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X-rays are produced in an x-ray tube. Figure 12.1 shows a schematic diagram of an x-ray tube.

An x-ray tube consists of an evacuated glass tubeevacuated glass tube to allow the electrons strike the electrons strike the

target without collisiontarget without collision with gas molecules.

12.1.2 Production of x-rays

Figure 12.1Figure 12.1

X-raysX-rays

Heated filament (cathode)

Tungsten target (anode)

Electrons

High voltage source

Cooling system

Evacuated glass tube

Power supply for heater

PHYSICS CHAPTER 12

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a heated filamentheated filament as a cathodecathode and is made from the made from the material of lower ionization energymaterial of lower ionization energy.

a target (anode) made from a heavy metal of high target (anode) made from a heavy metal of high melting pointmelting point such as tungsten and molybdenum.

a cooling systemcooling system that is used to prevent the target prevent the target (anode) from melting(anode) from melting.

a high voltage sourcehigh voltage source that is used to set the anode at a anode at a large positive potential compare to the filamentlarge positive potential compare to the filament.

When a filament (cathode) is heated by the current supplied to

it (filament current If), many electrons are emitted by

thermionic emissionthermionic emission (is defined as the emission of electrons the emission of electrons from a heated conductorfrom a heated conductor).

These electrons are accelerated towards a target, which is maintained at a high positive voltage relative to cathode.

The high speed electrons strike the target and rapidly decelerated on impact, suddenly the x-rays are emitted.

PHYSICS CHAPTER 12

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X-rays emissionX-rays emission can be considered as the reversereverse of the photoelectric effectphotoelectric effect. In the photoelectric effectphotoelectric effect, EM radiationEM radiation incident on a target causescauses the emission of electronsthe emission of electrons but in in an x-ray tubean x-ray tube, electronselectrons incident on a target cause the emission of EM radiation (x-rays)emission of EM radiation (x-rays).

The radiation produced by the x-ray tube is created by two completely difference physical mechanisms refer to: characteristiccharacteristic x-rays continuouscontinuous x-rays (called bremsstrahlungbremsstrahlung in german

which is braking radiationbraking radiation).

Characteristic x-raysCharacteristic x-rays The electrons which bombard the target are very energeticelectrons which bombard the target are very energetic

and are capable of knock out the inner shell electronsknock out the inner shell electrons from the target atom, creating the inner shell vacanciescreating the inner shell vacancies.

When these are refilled by electrons from the outer shellsrefilled by electrons from the outer shells, the electrons making a transitionelectrons making a transition from any one of the outer shells (higher energy level) to the inner shell (lower energy level) vacancies and emit the characteristic x-raysemit the characteristic x-rays.

PHYSICS CHAPTER 12

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The energy of the characteristic x-rays is given by

Since the energy of characteristic x-rays equal to the difference of the two energies level, thus its energy is discreteits energy is discrete . Then its frequency and wavelength also discretefrequency and wavelength also discrete.

Figure 12.2 shows the production of characteristic x-rays.

if EEhfE (12.1)(12.1)

KLM

vacancyvacancyHigh speed electronHigh speed electron

Electron in the shellElectron in the shellNucleusNucleus

11LK1

hchfEEE


22ML2

hchfEEE

PHYSICS CHAPTER 12

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Note:Note:

In the production of the x-rays, a target (anode) made from a heavy metal of multielectron atom, thus the energy level for multielectron atom is given by

Table 12.1 shows a shell designation for multielectron atom.

1,2,3,... ;

1eV 6.13

2

2

nn

ZEn (12.2)(12.2)

where (orbit) state of levelenergy : thnEnnumber atomic :Z

number quantum principal :n

n Shell Number of electron

1 K 2

2 L 8

3 M 18

4 N 32Table 12.1Table 12.1

PHYSICS CHAPTER 12

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Continuous x-rays (Bremsstrahlung)Continuous x-rays (Bremsstrahlung) Some of high speed electronshigh speed electrons which bombard the target

undergo a rapid decelerationundergo a rapid deceleration. This is braking. As the electrons suddenly come to rest in the targetelectrons suddenly come to rest in the target, a part

or all of their kinetic energies are converted into energy of kinetic energies are converted into energy of EM radiation immediatelyEM radiation immediately called Bresmsstrahlung, that is

These x-rays cover a wide range of wavelengths or frequencies and its energies are continuousenergies are continuous.

hfmv 2

2

1

EK

(12.3)(12.3)

energy of EM radiationkinetic energy of the electron

Note:Note: The intensity of x-raysintensity of x-rays depends on

the number of electrons hittingnumber of electrons hitting the target i.e. the filament filament currentcurrent.

the voltage across the tubevoltage across the tube. If the voltage increases so the energy of the bombarding electrons increases and therefore

makes more energy available for x-rays production.

PHYSICS CHAPTER 12

10

Calculate the minimum energy (in joule) of a bombarding electron

must have to knock out a K shell electron of a tungsten atom

(Z =74).

Solution :Solution :

By applying the equation of the energy level for multielectron atom,

For K shell,

For n =,

Therefore the minimum energy of the bombarding electron is given by

Example 1 :

fi ;1 nn

2

2

n

1eV 6.13

n

ZE

2

2

Ki1

174eV 6.13

EE

eV 1025.7 40f EE

if EEE 41025.70 E

J 1016.1 14E 194 1060.11025.7

PHYSICS CHAPTER 12

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Since there are two types of x-rays are produced in the x-ray tube, hence the x-ray spectra consist of line spectra line spectra (known as characteristic linescharacteristic lines) and continuous spectrumcontinuous spectrum as shown in Figure 12.3.

12.1.3 X-ray spectra


Line spectra (characteristic lines)

Continuous spectrum

X-ray intensity

Wavelength, 0min

31 2

αK

γKβK

min

No x-rays is produced if

The area under the graph = the total total intensity of x-raysintensity of x-rays

PHYSICS CHAPTER 12

12

At low applied voltagelow applied voltage across the tube, only a continuous continuous spectrum of radiation existsspectrum of radiation exists. As the applied voltage increasesincreases, groups of sharp peaks superimposed on the sharp peaks superimposed on the continuous radiation begin to appearcontinuous radiation begin to appear. These peaks are lines lines spectra spectra (characteristic lines) where it is dependdepend on the target target materialmaterial.

Characteristic linesCharacteristic lines The characteristic lines are the result of electrons transition

within the atoms of the target material due to the production of characteristic x-rays (section 12.1.2).

There are several types of characteristic lines series: KK lines series lines series is defined as the line spectra produced the line spectra produced

due to electron transition from outer shell to due to electron transition from outer shell to KK shell shell vacancyvacancy.

KK line line Electron transition from Electron transition from LL shell ( shell (n n =2) to =2) to

KK shell vacancy ( shell vacancy (nn =1) =1)

PHYSICS CHAPTER 12

13

LL lines series lines series is defined as the lines spectra produced the lines spectra produced

due to electron transition from outer shell to due to electron transition from outer shell to LL shell shell vacancy.vacancy.

KK line line Electron transition from Electron transition from MM shell ( shell (n n =3) =3)

to to KK shell vacancy ( shell vacancy (nn =1) =1)

KK line line Electron transition from Electron transition from NN shell ( shell (n n =4) =4)

to to KK shell vacancy ( shell vacancy (nn =1) =1)

LL line line Electron transition from Electron transition from NN shell ( shell (n n =4) =4)

to to LL shell vacancy ( shell vacancy (nn =2) =2)

LL line line Electron transition from Electron transition from OO shell ( shell (n n =5) =5)


LL line line Electron transition from Electron transition from MM shell ( shell (n n =3) =3)


MM lines series lines series is defined as the lines spectra produced the lines spectra produced

due to electron transition from outer shell to due to electron transition from outer shell to MM shell shell vacancy.vacancy.

PHYSICS CHAPTER 12

14KE

LE

MENEOEPE

1

2

3456n

(K shell)

(L shell)

(M shell)

(N shell)(O shell)(P shell)

These lines spectra can be illustrated by using the energy level diagram as shown in Figure 12.4.

MM line line Electron transition from Electron transition from OO shell ( shell (n n =5) =5)

to to MM shell vacancy ( shell vacancy (nn =3) =3)

MM line line Electron transition from Electron transition from PP shell ( shell (n n =6) to =6) to

MM shell vacancy ( shell vacancy (nn =3) =3)

MM line line Electron transition from Electron transition from NN shell ( shell (n n =4) =4)

to to MM shell vacancy ( shell vacancy (nn =3) =3)

αK

γK

βKαL

γL

βL αM

γM

βM


PHYSICS CHAPTER 12

15

These characteristic lines is the property of the target materialproperty of the target material i.e. for difference materialdifference material the wavelengths of the wavelengths of the characteristic lines are differentcharacteristic lines are different.

Note that the wavelengthswavelengths of the characteristic linescharacteristic lines does not not changeschanges when the applied voltageapplied voltage across x-ray tube changeschanges.

Continuous (background) spectrumContinuous (background) spectrum The continuous spectrum is produced by electrons colliding with

the target and being decelerated due to the production of continuous x-rays in section 12.1.2.

According to the x-ray spectra (Figure 12.3), the continuous spectrum has a minimum wavelength.

The existence of the minimum wavelengthexistence of the minimum wavelength is due to the emission of the most energetic photonenergetic photon where the kinetic kinetic energy of an electron acceleratedenergy of an electron accelerated through the x-ray tube is completely converted into the photon energy completely converted into the photon energy . This happens when the electronelectron colliding with the target is decelerated and decelerated and stoppedstopped in a single collisiona single collision.

PHYSICS CHAPTER 12

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If the electron is accelerated through a voltage V, the kinetic energy of the electron is

When the kinetic energy of the electron is completely converted

into the photon energy , thus the minimum wavelength minimum wavelength minmin

of the x-rays is

From the eq. (12.4), the minimum wavelength dependsminimum wavelength depends on the applied voltageapplied voltage across the x-ray tube and independentindependent of target materialtarget material.

UK eVK

electric potential energykinetic energy of the electron

EeV

minhc

eV

eV

hcmin (12.4)(12.4)

PHYSICS CHAPTER 12

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The strength of the x-rays are determined by their penetrating power.

The penetrating power depends on the wavelength of the x-penetrating power depends on the wavelength of the x-raysrays where if their wavelength are short then the penetrating power is high or vice versa.

By using the eq. (12.4) :

X-rays of low penetrating powerlow penetrating power are called softsoft x-ray and those of high penetrating powerhigh penetrating power are called hardhard x-ray.

12.1.4 Penetrating power (quality) of x-rays

eV

hc

V t

EP

hcE

P

Penetrating power

increasesincreases

decreasesdecreases

PHYSICS CHAPTER 12

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Filament currentFilament current When it is

increasedincreased, the intensity of the intensity of the x-ray spectra x-ray spectra also increasedalso increased as shown in Figure 12.5.

12.1.5 Factors influence the x-ray spectra

min 31 2

InitialInitial

FinalFinal

X-rays intensity

Wavelength, 0

No changeFigure 12.5Figure 12.5

PHYSICS CHAPTER 12

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Applied voltage (p.d.) across x-ray tubeApplied voltage (p.d.) across x-ray tube

InitialInitial

FinalFinal

When it is increasedincreased, the intensityintensity of the x-ray spectra also increasedincreased but the minimum minimum wavelengthwavelength is decreaseddecreased.

The wavelengths wavelengths of the of the characteristic characteristic lines remain lines remain unchangedunchanged as shown in Figure 12.6.

31 2i

X-rays intensity

Wavelength, 0f

No changeFigure 12.6Figure 12.6

PHYSICS CHAPTER 12

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Target materialTarget material

InitialInitial

FinalFinal


When the target material is changed with changed with heavy materialheavy material (greater in atomic greater in atomic numbernumber), the intensityintensity of the x-ray spectra increasedincreased, the wavelengths of wavelengths of the characteristic the characteristic lines decreasedlines decreased.

The minimum minimum wavelength wavelength remains remains unchangedunchanged as shown in Figure 12.7.

min31 2'

1'2 '

3

No change

X-rays intensity

Wavelength, 0

PHYSICS CHAPTER 12

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is from the production aspect as shown in Table 12.2.

12.1.6 Difference between x-ray emission spectra and optical atomic emission spectra

X-ray spectra Optical atomic spectra

is produced when the inner-most shell electron knocked out and left vacancy. This vacancy is filled by electron from outer shells.

The electron transition from outer shells to inner shell vacancy emits energy of x-rays and produced x-ray spectra.

is produced when the electron from ground state rises to the excited state.

After that, the electron return to the ground state and emits energy of EM radiation whose produced the emission spectra.

Table 12.2Table 12.2

PHYSICS CHAPTER 12

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Estimate the K wavelength for molybdenum (Z =42).

(Given the speed of light in the vacuum, c =3.00108 m s1 and Planck’s constant, h =6.631034 J s)


The energy level for K and L shells are

and

Example 2 :

42Z

2

21eV 6.13

n

ZEn

2

2

K1

142eV 6.13

E

eV 22862

2

2

L2

142eV 6.13

E

eV 5715

PHYSICS CHAPTER 12

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The difference between the energy level of K and L shells is

Therefore the wavelength corresponds to the E is given by

LK EEE

571522862

191060.117147 J 1074.2 15E

hc

E

83415 1000.31063.6

1074.2

m 1026.7 11

42Z

PHYSICS CHAPTER 12

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An x-ray tube has an applied voltage of 40 kV. Calculatea. the maximum frequency and minimum wavelength of the emitted x-rays,b. the maximum speed of the electron to produce the x-rays of maximum frequency.

(Given c =3.00108 m s1, h =6.631034 J s, me=9.111031 kg; e=1.601019 C and k=9.00109 N m2 C2)


a. The maximum frequency of the x-rays is

Example 3 :

V 1040 3V

eVhf max

319max

34 10401060.11063.6 f

Hz 1065.9 18max f

PHYSICS CHAPTER 12

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a. Since the frequency is maximum, thus the minimum wavelength

of x-rays is given by

b. The maximum speed of the electron is

18

8

1065.9

1000.3

m 1011.3 11min

V 1040 3V

maxmin f

c

18342max

31 1065.91063.61011.92

1 v

18max s m 1019.1 v

max2

max2

1hfmv

PHYSICS CHAPTER 12

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The energy of an electron in the various shells of the nickel atom is given by Table 12.3.

If the nickel is used as the target in an x-ray tube, calculate the

wavelength of the K line.

(Given the speed of light in the vacuum, c =3.00108 m s1 and Planck’s constant, h =6.631034 J s)

Example 4 :

Shell Energy (eV) 103

K 8.5

L 1.0

M 0.5

Table 12.3Table 12.3

PHYSICS CHAPTER 12

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The difference between the energy level of K and M shells is

Therefore the wavelength corresponds to the E is given by

MK EEE

33 105.0105.8

193 1060.1100.8 J 1028.1 15E

hc

E

83415 1000.31063.6

1028.1

m 1055.1 10

PHYSICS CHAPTER 12

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At the end of this chapter, students should be able to: At the end of this chapter, students should be able to: StateState Moseley’s Law and Moseley’s Law and explainexplain its impact on the its impact on the

periodic table.periodic table.

Learning Outcome:

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12.2 Moseley’s law (½ hour)

PHYSICS CHAPTER 12

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In 1913, Henry G.J. Moseley studies on the characteristic x-ray spectra for various target elements using the x-ray diffraction technique.

He found that the K frequency line in the x-ray spectra from a particular target element is varied smoothlyvaried smoothly with that element’s atomic number Z as shown in Figure 12.8.

12.2 Moseley’s law

21

Hz10 8K f

Z0 168 3224 40

16

8

24

AlAlSiSi

ClCl KK

TiTiVV

CrCrFeFe

CoCoNiNi

CuCuZnZn

ZrZrYY

1Figure 12.8Figure 12.8

PHYSICS CHAPTER 12

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From the Figure 12.8, Moseley states that the frequency of K frequency of K characteristic lines is proportional to the squared of atomic characteristic lines is proportional to the squared of atomic number for the target elementnumber for the target element and could be expressed as

Eq. (12.5) is known as Moseley’s lawMoseley’s law. Moseley’s law is considerable importance in the development development

of early quantum theory and the arrangement of modern of early quantum theory and the arrangement of modern periodic table of elementperiodic table of element (Moseley suggested the arrangement of the elements according to their atomic number,

Z).

215K 1Hz 1048.2 Zf (12.5)(12.5)

where line;K theoffrequency : Kfelement target theofnumber atomic: Z

PHYSICS CHAPTER 12

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For the K line of wavelength 0.0709 nm, determine the atomic

number of the target element.

(Given the speed of light in the vacuum, c =3.00108 m s1)


The frequency of the K line is given by

By applying the Moseley’s law, thus the atomic number for element is given by

Example 5 :

m 100709.0 9K

KK

cf

9

8

K 100709.0

1000.3

f

Hz 1023.4 18

215K 1Hz 1048.2 Zf

21518 11048.21023.4 Z42Z

PHYSICS CHAPTER 12

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At the end of this chapter, students should be able to: At the end of this chapter, students should be able to: DeriveDerive with the aid of a diagram the Bragg’s equation. with the aid of a diagram the Bragg’s equation. UseUse

Learning Outcome:

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12.3 X-ray diffraction (½ hour)

nd sin2

PHYSICS CHAPTER 12

33

12.3.1 Bragg’s law X-rays being diffracted by the crystal lattice if their wavelength

approximately equal to the distance between two consecutive atomic planes of the crystal.

The x-ray diffraction is shown by the diagram in Figure 12.9.

12.3 X-ray diffraction


RR

TT

AA

CC

OO

QQBB

PP

dsin dsin

i

d

airair

crystalcrystal

d

PHYSICS CHAPTER 12

34

From the Figure 12.9, the path difference L between rays RAC and TBO is given by

The path difference condition for constructive interference (brightbright) is

By equating the eqs. (12.6) and (12.7), hence

Eq. (12.8) is known as Bragg’s lawBragg’s law and the angle also known as Bragg angleBragg angle.

BQPBΔ LθdθdL sinsinΔ

θdL sin2Δ

,...3,2,1 ; Δ nnL

(12.6)(12.6)

(12.7)(12.7)

nd sin2 (12.8)(12.8)

whereplanes atomicbetween separation: d

rays- xof wavelength: ,...,, n 321order n diffractio:

or angleincident of complement (the angle glancing: angle)n diffractio

PHYSICS CHAPTER 12

35

Note:Note:

The number of diffraction order diffraction order nn depends on the glancing angle depends on the glancing angle

where if is increased then n also increased. The number of diffraction order diffraction order nn is maximum maximum when the glancing

angle =90=90. If n =1 1st order bright, the angle 1st order glancing angle If n =2 2nd order bright, the angle 2nd order glancing angle

12.3.2 Uses of x-rays In medicine, medicine, x-rays are used to diagnose illnessesdiagnose illnesses and for

treatmenttreatment. Soft x-raysSoft x-rays of low penetrating power are used for x-rays x-rays

photographyphotography. X-rays penetrate easily soft tissues such as the flesh, whereas the bonesbones which are high density high density and absorb more x-raysabsorb more x-rays. Hence the image of the bones on the photographic plate is less exposed compared to that of the soft tissues as shown in Figure 12.10.

PHYSICS CHAPTER 12

36

Hard x-raysHard x-rays are used in radio therapyradio therapy for destroying destroying cancerous cellscancerous cells. It is found that cancerous cells are more easily damaged by x-rays than stables ones.

In industry industry : x-rays are used to detect crackscracks in the interior of interior of a metala metal.

X-rays are used to study the structure of crystalstudy the structure of crystal by using x-ray spectrometry since they can be diffracted (Bragg’s lawBragg’s law).


PHYSICS CHAPTER 12

37

A beam of x-rays of wavelength 0.02 nm is incident on a crystal. The separation of the atomic planes in the crystal is 3.601010 m. Calculatea. the glancing angle for first order,b. the maximum number of orders observed.


a. Given

By using the Bragg’s law equation, thus

Example 6 :

m 1060.3 m; 1002.0 109 d1n

nd sin2

d

n

2sin 1

10

91

1060.32

1002.01sin

59.1

PHYSICS CHAPTER 12

38


b. The number of order is maximum when =90, thus

max90sin2 nd

d

n2

max

m 1060.3 m; 1002.0 109 d

nd sin2

9

10

1002.0

1060.32

36max n

PHYSICS CHAPTER 12

39

Curves A and B are two x-rays spectra obtained by using two different voltage. Based on the Figure 12.11 , answer the following questions.a. Explain and give reason, whether curves A and B are obtained by using the same x-ray tube.b. If curve B is obtained by using a voltage of 25 kV, calculate the voltage for curve A and obtained the Planck’s constant.

Example 7 :

0 1 2 3 4 5 6 7 8 9

Inte

nsi

tyA

B(25 kV)

(102 nm)Figure 12.11Figure 12.11

PHYSICS CHAPTER 12

40


a. For both curves, the characteristic lines spectra occurred at the

same value of wavelengths. That means the target material used

to obtain the curves A and B are the same but the applied

voltage is increased. Therefore the curves A and B are obtained

by using the same x-ray tube.

b. By applying the equation of minimum wavelength for continuous

x-ray,

For curve A:

For curve B:

V 1025 m; 100.5 m; 105.2 3B

11B

11A V

BB eV

hc

AA eV

hc (1)(1)

(2)(2)

PHYSICS CHAPTER 12

41


b. By dividing the eqs. (2) and (1) thus

By substituting the value of VA into the eq. (1) :

V 1020 m; 100.5 m; 105.2 3B

11B

11A V

A

B

A

B

eVhc

eVhc

B

A

A

B

V

V

3A

11

11

1025105.2

100.5

V

V 1050 3A V

319

811

10501060.1

1000.3105.2

h

s J 1067.6 34h

PHYSICS CHAPTER 12

42

Exercise 12.1 :Given c =3.00108 m s1, h =6.631034 J s, me=9.111031 kg

and e=1.601019 C

1. Electrons are accelerated from rest through a potential difference of 10 kV in an x-ray tube. Calculatea. the resultant energy of the electrons in electron-volt,b. the wavelength of the associated electron waves,c. the maximum energy and the minimum wavelength of the x-

rays generated.

ANS. :ANS. : 10 keV; 1.2310 keV; 1.2310101111 m; 1.60 m; 1.6010101515 J, 1.24 J, 1.2410101010 m m

2. An x-ray tube works at a DC potential difference of 50 kV. Only 0.4 % of the energy of the cathode rays is converted into x-rays and heat is generated in the target at a rate of 600 W. Determine

a. the current passed into the tube,

b. the velocity of the electrons striking the target.

ANS. :ANS. : 0.012 A; 1.330.012 A; 1.33101088 m s m s11

PHYSICS CHAPTER 12

43

Exercise 12.1 :3. Consider an x-ray tube that uses platinum (Z =78) as its

target.

a. Use the Bohr’s model to estimate the minimum kinetic

energy electrons ( in joule) must have in order for K

x- rays to just appear in the x-ray spectrum of the tube.

b. Assuming the electrons are accelerated from rest

through a voltage V, estimate the minimum voltage

required to produce the K x-rays.

(Physics, 3(Physics, 3rdrd edition, James S. Walker, Q54, p.1069) edition, James S. Walker, Q54, p.1069)

ANS. :ANS. : 1.291.2910101414 J; 80.6 J; 80.6101033 V V

4. A monochromatic x-rays are incident on a crystal for which the spacing of the atomic planes is 0.440 nm. The first order maximum in the Bragg reflection occurs when the angle between the incident and reflected x-rays is 101.2. Calculate the wavelength of the x-rays.

ANS. :ANS. : 5.595.5910101010 m m

44

PHYSICS CHAPTER 12

Next Chapter…CHAPTER 13 :

Nucleus

matriculation physics ( x-rays )

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