1/18

Generation and absorption of X rays

X ray crystallography

Attila Jenei

2/18

Electromagnetic spectrum

3/18

Atomic energy levels: the Bohr model

Bound electrons (those in atoms and molecules) are allowed to have only

certain energy levels: their energy is quantized (discrete).

.111 1

2

2

2

1

constRydbergRcmnn

R

Wavelength of transitions:

free (unbound) electrons with

• zero

• non-quantized

potential energy

atomic (bound) electrons with

• negative

• quantized

potential energy

emissionabsorption

tota

l e

ne

rgy

ion

iza

tio

n e

ne

rgy

(wo

rk f

un

cti

on

)

kinetic energy

ion

iza

tio

n

E1 E2 E3

12 EEhfEphoton

nucleus

Textbook, pages 25,26,32

4/18

• Electromagnetic radiation, energy is carried by photons, E=hf

Main features of X-rays

So why is it that special?

• Energy of X-ray photons is much greater than that of photons

of visible light

Generation of X-rays requires special conditions

-characteristic X-rays

-braking radiation

Absorption of X-rays is special

-photoeffect

-Compton effect (scattering)

-pair production

Absorption of X-ray means energy deposition in

the absorbing material, which may be damaged.

X-rays are a type of ionizing radiation, protection is required during X-ray exams

5/18

Wide range of medical applications

X-rays

conventional

planar X-ray

fluoroscopy

Computed

Tomography

radiotherapy

6/18

Fundamental questions

How are X-rays generated?

What are the mechanisms of X-ray absorption?

7/18

Generation of characteristic X rays, I

interaction of the accelerated electrons with orbital electrons of the

anode atoms

+accelerated electron

2

2

1mvEkin

1. the accelerated electron generates a

vacancy on an inner shell

2. the vacancy is filled by an electron on a

higher shell

3. the energy difference between the two

shells (e.g. EL-EK) is emitted as a photon

KL EEhf

K L M

anode heated cathode

(electron source)

+ -

X-rays

(characteristic and braking radiation)

electrons

Characteristic of the

anode material

X-ray tube

8/18

Generation of characteristic X rays, II

Ka, Kb, Kg

La, Lb

K

L

M

N

Energ

y L

evel (a

.u.)

ΔE1

ΔE2

ΔE3

ΔE1>ΔE2 >>ΔE3>>……

Vacancy must be created

in an inner shell,

otherwise ΔEx=hf would

not qualify for X-rays

9/18

Generation of braking radiation:

Interaction of accelerated electrons

with the nuclei of the anode

fmax (min) is observed when the

electron decelerates in a single

step.

++

+

+

2

12

1mv

2

22

1mv

2

32

1mv

2

42

1mv

2

2

2

112

1

2

1mvmvhf

2

3

2

222

1

2

1mvmvhf

2

4

2

332

1

2

1mvmvhf

eUmvc

hhf 2

1

min

max2

1

anode heated cathode

(electron source)

+ -

X-rays

(characteristic and braking radiation)

Typically 20-150 keV in diagnostics

electrons

1. electrons accelerated in the electric field

(applying acceleration voltage U) hit the anode

2. electrons gaining large kinetic energy

(1/2mv2=eU) interact with the nuclei of the

atoms in the anode

3. accelerating (=braking) charge generates

electromagnetic radiation (nucleus attracts

thereby slows electrons passing near by)

4. the greater the deceleration the greater the

energy of the generated photons, which at

high enough energy will be X-ray photons

X-ray tube

10/18

10 kV

20 kV

inte

nsity

25 kV

Ka

Kb

10 kV

20 kV

inte

nsity

min, 10 kVmin, 20 kV

1. Why isn’t the spectrum a sharp line?

Because the kinetic energy of the electron is

converted in several random steps to photons.

Because the maximum kinetic energy of the

electron increases.

2. Why does the limiting wavelength decrease with

increasing voltage?

Characteristics of the X-ray spectra

2

2

2

112

1

2

1mvmvhf

eUmvc

hhf 2

min

max2

1

3. Can one generate characteristic and braking

radiation simultaneously?

Yes, the accelerating voltage must be

increasedlarger kinetic energy of the

electronsgeneration of vacancies in inner

shells2

2

1mveU

4. Which X-ray is used in medical diagnostic

procedures?

The braking radiation, acceleration voltage

easily adjusts the energy of the radiation

11/18

Absorption of X-rays

12/18

Strong absorption (bones)

(high density, high Z atoms)

white on X-ray image

Weak absorption

(tissue containing air,

low density, low Z atoms)

dark on X-ray image

Absorption of X-rays and gamma-rays I.

Jo J

x

Absorbing material

Quantitative analysis of X-ray and gamma ray absorption, model system used:

The attenuation coefficient is

proportional to

~ absorber density

~ (Zeff)3, Zeff:effective atomic

number of the absorber

13/18

0 0.5 1 1.5 2-10

-8

-6

-4

-2

0

Absorption of X-rays and gamma-rays II.

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

x

oJ J e x

o

Je

J

o

J

J

x

lno

Jx

J

Jo – incident intensity

J – intensity after passing through

the material of thickness x

(= at penetration depth x)

lno

J

J

where x=1/

x1/

0.36

Slope of the line: -

Jo J

x

absorbing material

1

1 0.3679o

Je e

J

– attenuation coefficientt ([]=1/m)

bones (Cu on practical)

Connective tissue

(Al on practical)

Cu>Al

The attenuation coefficient is the

reciprocal of the distance where the

intensity of the radiation decreases to

e-1 times the initial value.

14/18

The most important mechanisms leading to the absorption of X rays and gamma rays:

1. Photoeffect: the photon is absorbed and imparts all of its energy to the

atom leading to the ejection of an electron.

+ K L M

X-ray photon

ejected electron

kineticEAhf A – ionization energy

Absorption of X-rays and gamma-rays III.

2

m

3

3

eff

3

τ: attenuation coefficient for photoeffect

τ :mass attenuation coefficient for photoeffect, cm /g

ρ: density, g/cm

Z : effective atomic number

;m m effZ

15/18

2. Compton effect: the photon transfers part of its energy to an outer

(loosely bound) electron. The electron is ejected, the photon is deflected and

its frequency decreases.

+ K L M

X-ray photon (f)

scattered X-ray photon (f’)

Compton electron

2

2

1' eevmAhfhf

The most important mechanisms leading to the absorption of X-rays and gamma-rays:

Absorption of X-rays and gamma-rays IV.

2

m

3

eff

: attenuation coefficient for Compton scattering

:mass attenuation coefficient for Compton scattering, cm /g

ρ: density, g/cm

Z : effective atomic and mass numbers

;

,A

m m

eff

eff

Z

A

16/18

3. Pair production: the photon is converted to an electron-positron pair near

a heavy nucleus.

+ K L M

electron

positron

The nucleus is pushed

away, thereby taking

up part of the

momentum of the

photon.

electron

annihilation: the positron

collides with an electron

and they are converted to

a pair of gamma photons.

2

min cmmhf positronelectron

the energy of the photon has to

cover the energy equivalent to the

rest masses of the electron and the

positron

MeVJ

smkgcm

mm

electron

positronelectron

02.11064.1

/103101.922

13

28312

Pair production takes

place only above 1.02

MeV energy (gamma

rays, HARD X-rays)

The most important mechanisms leading to the absorption of X-rays and gamma rays:

Absorption of X-rays and gamma-rays V.

17/18

X-ray beam

crystal

interference pattern

on the screen

bright spots generated as

a result of constructive

interference

• A technique based on the diffraction/reflection of X-rays

from crystals generating an interference pattern.

• From the interference pattern the structure of crystals

can be determined.

• Crystal: an ordered 3D array of atoms, ions, molecules

NaCl crystal

unit cell: the

repeating unit in

the crystal

• When atoms, molecules, ions in the

crystal are exposed to X-rays, they

scatter the radiation in all directions.

• In most of these directions the beams

won’t be visible due to destructive

interference

• There will be a few directions in which

constructive interference is generated

and the rays will be visible. Crystal

structure has to be determined based

on these directions.

X-ray crystallography I

18/18

c

X-ray beam

atoms, ions, molecules

(scattering centers)

g lcs cos

g1

g 1cos 1cs. g 2cos 2cs

g2

.

X-ray crystallography II

19/18

s1

s2

g

g0

gg lcsss coscos 021

c

X-ray crystallography III

20/18

gg lc coscos 0

bb kb coscos 0

aa ha coscos 0

1coscoscos 222 gba

The system of equations is overdetermined (3 unknowns (a,b,c), 4

equations). Solution is only possible in special cases.

1. Rotation method

2. Crystal powder method

X-ray crystallography IV

21/18

X-ray crystallography V

Interpretation according to Bragg

a

a lds cos2d

22/18

X-ray crystallography VI

Determination of the conformation (structure) of molecules

• Using the methods discussed so far it is possible to determine the

distance of unit cells in the lattice, but not their internal structure.

• In a molecular lattice a molecule occupies a unit cell, therefore the

internal structure of a unit cell has to be determined.

s2

s1

21 sss

unit cell

The intensity of reflections is

determined by the internal

structure of the unit cell.

X-ray diffraction image

molecular structure

sinterference

patterncrystal structure

23/18

X-ray crystallography VII

3D structure of an ion channel

X-ray crystallography has been used for the determination of

the 3D structure of proteins and nucleic acids since its

conception.

24/18

The structure of gefitinib

PLAY

• The overexpression of epidermal growth factor receptor

(EGFR) plays a role in the development of certain human

cancers.

• EGFR possesses tyrosine kinase activity, which leads to

the induction of cell proliferation in multiple steps.

• A drug called gefitinib (Iressa®) specifically inhibits the

tyrosine kinase activity of EGFR.

Gefitinib fits nicely into the ATP binding cleft of EGFR.

X-ray crystallography VIII

The 3D structure of proteins is used in rational drug design