matriculation physics x rays.pdf

8/12/2019 Matriculation Physics X rays.pdf

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1

PHYSICS CHAPTER 12

is defined as an electromagnetican electromagnetic

radiation of shorter wavelengthradiation of shorter wavelengththan UV radiation produced bythan UV radiation produced bythe bombardment of atoms bythe bombardment of atoms byhigh energy electrons in x-rayhigh energy electrons in x-ray

tubetube .

CHAPTER 12: X-raysCHAPTER 12: X-rays

(2 Hours)(2 Hours)

disco ered !yWilhelm Konrad RontgenWilhelm Konrad Rontgen

in 1"#$.


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PHYSICS CHAPTER 12

2

At the end of this chapter, students should be able toAt the end of this chapter, students should be able to!xplain!xplain with the aid of a diagram, the production ofwith the aid of a diagram, the production of"-rays from an "-ray tube#"-rays from an "-ray tube#

!xplain!xplain the production of continuous and characteristicthe production of continuous and characteristic"-ray spectra#"-ray spectra#$erive and use$erive and use the formulae for minimum wavelength forthe formulae for minimum wavelength forcontinuous "-ray spectra,continuous "-ray spectra,

%dentify%dentify the effects of the variation of current,the effects of the variation of current,accelerating voltage and atomic number of the anode onaccelerating voltage and atomic number of the anode onthe continuous and characteristic "-ray spectra#the continuous and characteristic "-ray spectra#

&earning 'utcome

% % %

. & ' ( )

. ' a * r

i & . e

d u

. ' y + (

) y s i c s

% % %

. & ' ( )

. ' a * r

i & . e

d u

. ' y + (

) y s i c s 12.1 X-ray s ec*ra ( 1 our)

eV hc=min


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PHYSICS CHAPTER 12

3

()#(#( *roperties of x-raysI*s ro er*ies are

,-rays *ra e in a straight linesstraight lines a* * e speed of lightspeed of light .,-rays cannotcannot !e deflecteddeflected !y electricelectric or magnetic fieldsmagnetic fields .

(T is is con incin e idence * a* * ey are unc ar ed orneutral particlesneutral particles ),-rays can !e diffracteddiffracted !y * e crystal latticecrystal lattice if * e s acin!e*%een *%o consecu*i e anes of a*o's a ro,i'a*e ye/ua *o i*s %a e en * .

,-rays affect photographic filmaffect photographic film .,-rays can roduce fluorescencefluorescence and photoelectricphotoelectricemissionemission .,-rays penetrate matter penetrate matter . Pene*ra*ion o%er is leastleast in * ematerials of high densitymaterials of high density .

()#( "-ray spectra


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PHYSICS CHAPTER 12

4

X-rays are roduced in an ,-ray *u!e. 0i ure 12.1 s o%s asc e'a*ic dia ra' of an ,-ray *u!e.

An ,-ray *u!e consis*s of an evacuated glass tubeevacuated glass tube *o a o% * e electrons stri+e theelectrons stri+e thetarget without collisiontarget without collision %i* as 'o ecu es.

()#(#) *roduction of x-rays

igure ()#(igure ()#(

"-rays"-rays

Hea*ed fi a'en*(ca* ode)

Tun s*en *ar e*(anode)

E ec*rons

Hi o *a e source

Coo in sys*e'

E acua*ed ass*u!e

Po%er su yfor ea*er


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PHYSICS CHAPTER 12

5

a heated filamentheated filament as a cathodecathode and is made from themade from thematerial of lower ioni ation energymaterial of lower ioni ation energy .

a target .anode/ made from a heavy metal of hightarget .anode/ made from a heavy metal of highmelting pointmelting point suc as *un s*en and 'o y!denu'.a cooling systemcooling system * a* is used *o prevent the targetprevent the target.anode/ from melting.anode/ from melting .a high voltage sourcehigh voltage source * a* is used *o se* * e anode at aanode at alarge positive potential compare to the filamentlarge positive potential compare to the filament .

en a fi a'en* (ca* ode) is ea*ed !y * e curren* su ied *oi* (fi a'en* curren* I f ) 'any e ec*rons are e'i**ed !y thermionicthermionicemissionemission (is defined as the emission of electrons from athe emission of electrons from a

heated conductor heated conductor ).T ese e ec*rons are acce era*ed *o%ards a *ar e* % ic is'ain*ained a* a i osi*i e o *a e re a*i e *o ca* ode.T e i s eed e ec*rons s*ri&e * e *ar e* and ra id ydece era*ed on i' ac* sudden y * e ,-rays are e'i**ed.


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PHYSICS CHAPTER 12

6

"-rays emission"-rays emission can !e considered as * e reversereverse of * ephotoelectric effectphotoelectric effect . In * e photoelectric effectphotoelectric effect !0 radiation!0 radiation

inciden* on a *ar e* causescauses the emission of electronsthe emission of electrons !u* ininan x-ray tubean x-ray tube electronselectrons inciden* on a *ar e* cause * eemission of !0 radiation .x-rays/emission of !0 radiation .x-rays/ .T e radia*ion roduced !y * e ,-ray *u!e is crea*ed !y *%oco' e*e y difference ysica 'ec anis's refer *o:

characteristiccharacteristic ,-rayscontinuouscontinuous ,-rays (ca ed bremsstrahlungbremsstrahlung in er'an % icis bra+ing radiationbra+ing radiation ).

1haracteristic x-rays1haracteristic x-raysT e electrons which bombard the target are very energeticelectrons which bombard the target are very energetic and are ca a! e of +noc+ out the inner shell electrons+noc+ out the inner shell electrons fro'* e *ar e* a*o' creating the inner shell vacanciescreating the inner shell vacancies .en * ese are refilled by electrons from the outer shellsrefilled by electrons from the outer shells

* e electrons ma+ing a transitionelectrons ma+ing a transition fro' any one of * e ou*ers e s ( i er ener y e e ) *o * e inner s e ( o%er ener y e e )acancies and emit the characteristic x-raysemit the characteristic x-rays .


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PHYSICS CHAPTER 12

7

T e ener y of * e c arac*eris*ic ,-rays is i en !y

Since * e ener y of c arac*eris*ic ,-rays e/ua *o * e differenceof * e *%o ener ies e e * us its energy is discreteits energy is discrete . T en i*sfre2uency and wavelength also discretefre2uency and wavelength also discrete .0i ure 12.2 s o%s * e roduc*ion of c arac*eris*ic ,-rays.

if E E hf E == .()#(/.()#(/

K LM

vacancyvacancy3igh speed electron3igh speed electron

!lectron in the shell!lectron in the shell4ucleus4ucleus

1

1LK 1

hchf E E E ===

igure ()#)igure ()#)

22ML2

hchf E E E ===


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PHYSICS CHAPTER 12

8

4ote4ote

In * e roduc*ion of * e ,-rays a *ar e* (anode) 'ade fro' a ea y'e*a of 'u *ie ec*ron a*o' * us * e ener y e e for 'u *ie ec*rona*o' is i en !y

Ta! e 12.1 s o%s a s e desi na*ion for 'u *ie ec*ron a*o'.

( ) ( ) 1,2,3,...;1eV6.13 22

=

= nn

Z E n .()#)/.()#)/

% ere (orbit)stateof levelenergy: thn E nn mber atomi!: Z

n mber " ant m #rin!i#al:n

n 5hell 4umber of electron

1 K 2

2 L "

3 M 1"

4 $ 326able ()#(6able ()#(


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PHYSICS CHAPTER 12

9

1ontinuous x-rays .7remsstrahlung/1ontinuous x-rays .7remsstrahlung/So'e of high speed electronshigh speed electrons % ic !o'!ard * e *ar e*

undergo a rapid decelerationundergo a rapid deceleration . T is is !ra&in . As * e electrons suddenly come to rest in the targetelectrons suddenly come to rest in the target a ar* ora of * eir +inetic energies are converted into energy of !0+inetic energies are converted into energy of !0radiation immediatelyradiation immediately ca ed 5res'ss*ra un * a* is

T ese ,-rays co er a %ide ran e of %a e en * s or fre/uenciesand i*s energies are continuousenergies are continuous .

hf mv =22

1

E K =

.()#8/.()#8/

ener y of E6 radia*ion&ine*ic ener y of * e e ec*ron

4ote4ote

T e intensity of x-raysintensity of x-rays de ends on* e number of electrons hittingnumber of electrons hitting * e *ar e* i.e. * e filamentfilament

currentcurrent .* e voltage across the tubevoltage across the tube . If * e o *a e increases so * e

ener y of * e !o'!ardin e ec*rons increases and * erefore 'a&es'ore ener y a ai a! e for ,-rays roduc*ion.


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PHYSICS CHAPTER 12

10

Ca cu a*e * e 'ini'u' ener y (in 7ou e) of a !o'!ardin e ec*ron'us* a e *o &noc& ou* a K s e e ec*ron of a *un s*en a*o'( Z 894).

5olution 5olution 5y a yin * e e/ua*ion of * e ener y e e for 'u *ie ec*ron a*o'

0or K s e

0or n 8T erefore * e 'ini'u' ener y of * e !o'!ardin e ec*ron is i en!y

E,a' e 1 :

== f i ;1 nn

( ) ( )22

n1eV6.13

n Z E =

( ) ( )2

2

K i1

1%&eV6.13

== E E eV1'2.% &=

'f == E E

if E E E = ( )&1'2.%' = E

1'16.1 1&= E ( )( )1*& 1'6'.11'2.% =


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PHYSICS CHAPTER 12

11

Since * ere are *%o *y es of ,-rays are roduced in * e ,-ray*u!e ence * e ,-ray s ec*ra consis* of line spectraline spectra (&no%n ascharacteristic linescharacteristic lines ) and continuous spectrumcontinuous spectrum as s o%n in0i ure 12.3.

()#(#8 "-ray spectra

igure ()#8igure ()#8

ine s ec*ra(c arac*eris*ic ines)

Con*inuouss ec*ru'

X-ray in*ensi*y

a e en *

'min

3

1 2

+K

K -K

min .

3 1 2 i

X-ra ys in*ensi*y

a e en *

'f

;o c an eigure ()#


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PHYSICS CHAPTER 12

20

6arget material6arget material

%nitial%nitialinalinal

igure ()#=igure ()#=

en * e *ar e*

'a*eria ischanged withchanged withheavy materialheavy material (greater in atomicgreater in atomicnumber number ) * eintensityintensity of * e ,-

ray s ec*raincreasedincreased * ewavelengths ofwavelengths ofthe characteristicthe characteristiclines decreasedlines decreased .T e minimumminimumwavelengthwavelengthremainsremainsunchangedunchanged ass o%n in 0i ure12.9.

min

3 1 2 01

02

03

;o c an e

X-rays in*ensi*y

a e en *

'


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PHYSICS CHAPTER 12

21

is fro' * e roduc*ion as ec* as s o%n in Ta! e 12.2.

()#(#< $ifference between x-ray emission spectraand optical atomic emission spectra

"-ray spectra 'ptical atomic spectra

is roduced % en * einner-'os* s e e ec*ron&noc&ed ou* and ef*acancy. T is acancy isfi ed !y e ec*ron fro' ou*ers e s.T e e ec*ron *ransi*ion fro'

ou*er s e s *o inner s eacancy e'i*s ener y of ,-rays and roduced ,-rays ec*ra.

is roduced % en * ee ec*ron fro' rounds*a*e rises *o * e e,ci*eds*a*e.

Af*er * a* * e e ec*ronre*urn *o * e round s*a*eand e'i*s ener y of E6

radia*ion % ose roduced* e e'ission s ec*ra.

6able ()#)6able ()#)


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PHYSICS CHAPTER 12

22

Es*i'a*e * e K %a e en * for 'o y!denu' ( Z 842).

(?i en * e s eed of i * in * e acuu' c 83.@@ 1@" ' s 1andP anc& s cons*an* h 8>.>3 1@34 B s)

5olution 5olution

T e ener y e e for K and L s e s are

and

E,a' e 2 :

&2= Z

( ) ( )2

21eV6.13

n Z

E n=

( ) ( )2

2

K 1

1&2eV6.13

= E

eV22 62=( ) ( )

2

2

L2

1&2eV6.13

= E eV%1=


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PHYSICS CHAPTER 12

23

5olution 5olution

T e difference !e*%een * e ener y e e of K and L s e s is

T erefore * e %a e en * corres onds *o * e E is i en !y

LK E E E =( ) ( )%122 62 =( )( )1*1'6'.11%1&% =

1'%&.21

= E

hc E =

( )( ) 3&

1 1'''.31'63.61'%&.2 =

m1'26.% 11=

&2= Z


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PHYSICS CHAPTER 12

24

An ,-ray *u!e as an a ied o *a e of 4@ & . Ca cu a*ea. * e 'a,i'u' fre/uency and 'ini'u' %a e en * of * e e'i**ed

,-rays!. * e 'a,i'u' s eed of * e e ec*ron *o roduce * e ,-rays of 'a,i'u' fre/uency.(?i en c 83.@@ 1@" ' s 1 h 8>.>3 1@34 B s m e8#.11 1@31 & De 81.>@ 1@1# C and k 8#.@@ 1@# ; ' 2 C 2)

5olution 5olution a. T e 'a,i'u' fre/uency of * e ,-rays is

E,a' e 3 :

V1'&' 3=V

eV hf =ma( ) ( )( )31*ma3& 1'&'1'6'.11'63.6 = f

41'6.* 1ma = f


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PHYSICS CHAPTER 12

25

5olution 5olution a. Since * e fre/uency is 'a,i'u' * us * e 'ini'u' %a e en *

of ,-rays is i en !y

!. T e 'a,i'u' s eed of * e e ec*ron is

1

1'6.*

1'''.3

=m1'11.3 11min

=

V1'&' 3=V

mamin f

c=

( ) ( )( )13&2ma31 1'6.*1'63.61'11.*21 = v

1ma sm1'1*.1

=v

ma2

ma21

hf mv =


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PHYSICS CHAPTER 12

26

T e ener y of an e ec*ron in * e arious s e s of * e nic&e a*o' isi en !y Ta! e 12.3.

If * e nic&e is used as * e *ar e* in an ,-ray *u!e ca cu a*e * e%a e en * of * e K ine.

(?i en * e s eed of i * in * e acuu' c 83.@@ 1@" ' s 1andP anc& s cons*an* h 8>.>3 1@34 B s)

E,a' e 4 :

5hell !nergy .eV/ (> 8

K ".$L 1.@M @.$

6able ()#86able ()#8


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PHYSICS CHAPTER 12

27

5olution 5olution

T e difference !e*%een * e ener y e e of K and M s e s is

T erefore * e %a e en * corres onds *o * e E is i en !y

MK E E E =( ) ( )33 1'.'1'. =( )( )1*3 1'6'.11''. =

1'2.11

= E

hc E =

( )( ) 3&

1 1'''.31'63.61'2.1 =

m1'.1 1'=


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PHYSICS CHAPTER 12

28

At the end of this chapter, students should be able toAt the end of this chapter, students should be able to5tate5tate 0oseley?s &aw and0oseley?s &aw and explainexplain its impact on theits impact on theperiodic table#periodic table#

&earning 'utcome

% % %

. & ' ( )

. ' a * r

i & . e

d u

. ' y + (

) y s i c

s

% % %

. & ' ( )

. ' a * r

i & . e d

u . '

y + (

) y s i c

s

12.2 6ose ey s a% ( our)


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PHYSICS CHAPTER 12

29

In 1#13 Henry ?.B. 6ose ey s*udies on * e c arac*eris*ic ,-rays ec*ra for arious *ar e* e e'en*s usin * e ,-ray diffrac*ion*ec ni/ue.

He found * a* * e K fre/uency ine in * e ,-ray s ec*ra fro' aar*icu ar *ar e* e e'en* is varied smoothlyvaried smoothly %i* * a* e e'en* sa*o'ic nu'!er Z as s o%n in 0i ure 12.".

()#) 0oseley?s law

21

41'K f

Z ' 16 322& &'

16

2&

AlAl 5i5i

1l1l KK

6i6iVV

1r 1r ee1o1o

4i4i

1u1u@n@n

@r @r

1igure ()#Bigure ()#B


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PHYSICS CHAPTER 12

30

0ro' * e 0i ure 12." 6ose ey s*a*es * a* * e fre2uency of Kfre2uency of Kcharacteristic lines is proportional to the s2uared of atomiccharacteristic lines is proportional to the s2uared of atomic

number for the target elementnumber for the target element and cou d !e e, ressed as

E/. (12.$) is &no%n as 0oseley?s law0oseley?s law .6ose ey s a% is considera! e i' or*ance in * e developmentdevelopmentof early 2uantum theory and the arrangement of modernof early 2uantum theory and the arrangement of modern

periodic table of elementperiodic table of element (6ose ey su es*ed * earran e'en* of * e e e'en*s accordin *o * eir a*o'ic nu'!er Z ).

( )( )21K 141'&.2 = Z f .()#;/.()#;/% ere line;Ktheof fre" en!y:K f

elementtargettheof n mberatomi!: Z


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PHYSICS CHAPTER 12

31

0or * e K ine of %a e en * @.@9@# n' de*er'ine * e a*o'ic

nu'!er of * e *ar e* e e'en*.

(?i en * e s eed of i * in * e acuu' c 83.@@ 1@" ' s 1)

5olution 5olution

T e fre/uency of * e K ine is i en !y

5y a yin * e 6ose ey s a% * us * e a*o'ic nu'!er for e e'en*is i en !y

E,a' e $ :

m1''%'*.' *K =

K K

c f = *K 1''%'*.'1'''.3

= f

41'23.& 1=

( )( )21K 141'&.2 = Z f ( )( )211 11'&.21'23.& = Z &2= Z


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PHYSICS CHAPTER 12

32

At the end of this chapter, students should be able toAt the end of this chapter, students should be able to$erive$erive with the aid of a diagram the 7ragg?s e2uation#with the aid of a diagram the 7ragg?s e2uation#UseUse

&earning 'utcome

% % %

. & ' ( )

. ' a * r

i & . e d

u . '

y + (

) y s i c

s

% % %

. & ' (

) . '

a * r

i & . e d

u . '

y + (

) y s i c

s

12.3 X-ray diffrac*ion ( our)

nd =sin2


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PHYSICS CHAPTER 12

33

()#8#( 7ragg?s lawX-rays !ein diffrac*ed !y * e crys*a a**ice if * eir %a e en *a ro,i'a*e y e/ua *o * e dis*ance !e*%een *%o consecu*i ea*o'ic anes of * e crys*a .T e ,-ray diffrac*ion is s o%n !y * e dia ra' in 0i ure 12.#.

()#8 "-ray diffraction

igure ()#Cigure ()#C

RR

66AA

11

''

DD77

**

dsin dsin

i

d

air air

crystalcrystal

d


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PHYSICS CHAPTER 12

34

0ro' * e 0i ure 12.# * e a* difference L !e*%een raysRAC and T5= is i en !y

T e a* difference condi*ion for cons*ruc*i e in*erference(brightbright ) is5y e/ua*in * e e/s. (12.>) and (12.9) ence

E/. (12.") is &no%n as 7ragg?s law7ragg?s law and * e an e a so&no%n as 7ragg angle7ragg angle .

5/57 += L d d L sinsin7 +=

d L sin27 =,...3,2,1;7 == nn L

.()#


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PHYSICS CHAPTER 12

35

4ote4ote

T e nu'!er of diffraction orderdiffraction order nn depends on the glancing angledepends on the glancing angle% ere if is increased * en n a so increased.

T e nu'!er of diffraction orderdiffraction order nn is maximummaximum % en * e ancinan e 9C>9C>.

If n 81 1 s* order !ri * * e an e 1 s* order ancin an e

If n 82 2 nd order !ri * * e an e 2 nd order ancin an e

()#8#) Uses of x-raysIn medicine,medicine, ,-rays are used *o diagnose illnessesdiagnose illnesses and fortreatmenttreatment .

5oft x-rays5oft x-rays of o% ene*ra*in o%er are used for x-raysx-raysphotographyphotography . X-rays ene*ra*e easi y sof* *issues suc as* e f es % ereas * e bonesbones % ic are high densityhigh density and absorb more x-raysabsorb more x-rays . Hence * e i'a e of * e !ones on * eo*o ra ic a*e is ess e, osed co' ared *o * a* of * e

sof* *issues as s o%n in 0i ure 12.1@.


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PHYSICS CHAPTER 12

36

3ard x-rays3ard x-rays are used in radio therapyradio therapy for destroyingdestroyingcancerous cellscancerous cells . I* is found * a* cancerous ce s are 'oreeasi y da'a ed !y ,-rays * an s*a! es ones.

In industryindustry : ,-rays are used *o de*ec* crac+scrac+s in * e interior ofinterior ofa metala metal .

X-rays are used *o study the structure of crystalstudy the structure of crystal !y usin ,-ray s ec*ro'e*ry since * ey can !e diffrac*ed ( 7ragg?s law7ragg?s law ).

igure ()#(>igure ()#(>


37/44

PHYSICS CHAPTER 12

37

A !ea' of ,-rays of %a e en * @.@2 n' is inciden* on a crys*a .T e se ara*ion of * e a*o'ic anes in * e crys*a is 3.>@ 1@1@ '.Ca cu a*ea. * e ancin an e for firs* order!. * e 'a,i'u' nu'!er of orders o!ser ed.5olution 5olution a. ?i en 5y usin * e 5ra s a% e/ua*ion * us

E,a' e > :

m1'6'.3m;1''2.' 1'* == d 1=n

nd =sin2

= d

n

2sin 1

( )( )

=

1'

*1

1'6'.321''2.'1

sin

*.1=


38/44

PHYSICS CHAPTER 12

38

5olution 5olution

!. T e nu'!er of order is 'a,i'u' % en 8#@ * us

ma*'sin2 nd =

d n

2ma =

m1'6'.3m;1''2.' 1'* == d

nd =sin2

( )*

1'

1''2.'1'6'.32

=

36ma =n


39/44

PHYSICS CHAPTER 12

39

Cur es A and 5 are *%o ,-rays s ec*ra o!*ained !y usin *%o

differen* o *a e. 5ased on * e 0i ure 12.11 ans%er * e fo o%in/ues*ions.a. E, ain and i e reason % e* er cur es A and 5 are o!*ained

!y usin * e sa'e ,-ray *u!e.!. If cur e 5 is o!*ained !y usin a o *a e of 2$ & ca cu a*e * e

o *a e for cur e A and o!*ained * e P anc& s cons*an*.

E,a' e 9 :

@ 1 2 3 4 $ > 9 " #

I n * e n

s i * y

A

5(2$ & )

( 1@2 n')igure ()#((igure ()#((


40/44

PHYSICS CHAPTER 12

40

5olution 5olution a. 0or !o* cur es * e c arac*eris*ic ines s ec*ra occurred a* * e

sa'e a ue of %a e en * s. T a* 'eans * e *ar e* 'a*eria used

*o o!*ain * e cur es A and 5 are * e sa'e !u* * e a iedo *a e is increased. T erefore * e cur es A and 5 are o!*ained!y usin * e sa'e ,-ray *u!e.

!. 5y a yin * e e/ua*ion of 'ini'u' %a e en * for con*inuous,-ray

0or cur e A:

0or cur e 5:

V1'2m;1''.m;1'.2 3511

511 === V

55 eV

hc

=

eV hc= .(/.(/

.)/.)/


41/44

PHYSICS CHAPTER 12

41

5olution 5olution !. 5y di idin * e e/s. (2) and (1) * us

5y su!s*i*u*in * e a ue of V ; in*o * e e/. (1) :

V1'2'm;1''.m;1'.2 3511

511 === V

= 55

eV hc

eV hc

5

5

V V =

311

11

1'21'.21''.

=

V

V1'' 3 =V

( )( )( )31*

11

1''1'6'.11'''.3

1'.2

= h

s1'6%.6 3&=h


42/44


43/44

PHYSICS CHAPTER 12

43

E,ercise 12.1 :3. Consider an ,-ray *u!e * a* uses a*inu' ( Z 89") as i*s

*ar e*.a. Gse * e 5o r s 'ode *o es*i'a*e * e 'ini'u' &ine*icener y e ec*rons ( in 7ou e) 'us* a e in order for K ,-rays *o 7us* a ear in * e ,-ray s ec*ru' of * e *u!e.!. Assu'in * e e ec*rons are acce era*ed fro' res* * rou

a o *a e V es*i'a*e * e 'ini'u' o *a e re/uired *oroduce * e K ,-rays.

.*hysics, 8.*hysics, 8 rdrd edition, Fames 5# Wal+er, D;:, p#(>(> (:(: FE B>##(> 88 VV

4. A 'onoc ro'a*ic ,-rays are inciden* on a crys*a for % ic* e s acin of * e a*o'ic anes is @.44@ n'. T e firs* order'a,i'u' in * e 5ra ref ec*ion occurs % en * e an e!e*%een * e inciden* and ref ec*ed ,-rays is [email protected] . Ca cu a*e* e %a e en * of * e ,-rays.

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