This document discusses x-rays and their production and spectra. It begins by defining x-rays as electromagnetic radiation produced when high-energy electrons bombard atoms. X-rays were discovered in 1895 by Wilhelm Röntgen. The document then discusses how x-rays are produced in an x-ray tube, where high-speed electrons are accelerated toward a metal target. This produces two types of x-rays: characteristic x-rays formed by electron transitions within atoms, and continuous x-rays formed when electrons are decelerated. The x-ray spectrum consists of characteristic line spectra and a continuous spectrum. It provides formulas for calculating x-ray energies and wavelengths.
The Rydberg formula helps to determine the wavenumber or wavelengths of hydrogen spectral lines obtained in the hydrogen spectrum. Previously, Johann Jakob Balmer discovered an empirical formula to determine the wavelengths of hydrogen spectral lines obtained in the visible region of the hydrogen spectrum. As we all know, the hydrogen spectrum is not limited to the visible zone only. It occupies the ultraviolet and infrared parts of the electromagnetic spectrum also. Hence, the scientists' quests to determine the spectral positions of various spectral lines of the hydrogen spectrum finally came to an end with the Rydberg formula.
For more information on this topic, kindly visit our blog at;
https://jayamchemistrylearners.blogspot.com/2022/05/rydberg-ritz-combination-principle.html
The Rydberg formula helps to determine the wavenumber or wavelengths of hydrogen spectral lines obtained in the hydrogen spectrum. Previously, Johann Jakob Balmer discovered an empirical formula to determine the wavelengths of hydrogen spectral lines obtained in the visible region of the hydrogen spectrum. As we all know, the hydrogen spectrum is not limited to the visible zone only. It occupies the ultraviolet and infrared parts of the electromagnetic spectrum also. Hence, the scientists' quests to determine the spectral positions of various spectral lines of the hydrogen spectrum finally came to an end with the Rydberg formula.
For more information on this topic, kindly visit our blog at;
https://jayamchemistrylearners.blogspot.com/2022/05/rydberg-ritz-combination-principle.html
Transmission electron microscope, high resolution tem and selected area elect...Nano Encryption
The transmission electron microscope is a very powerful tool for material science. A high energy beam of electrons is shone through a very thin sample, and the interactions between the electrons and the atoms can be used to observe features such as the crystal structure and features in the structure like dislocations and grain boundaries. Chemical analysis can also be performed. TEM can be used to study the growth of layers, their composition and defects in semiconductors. High resolution can be used to analyze the quality, shape, size and density of quantum wells, wires and dots.
This presentation covers basics of thermoelectrics with major effects. It also includes applications part of thermoelectrics and some selection criterias for designing TE devices for maximum efficiency.
The following presentation consists of introduction to dielectrics, and includes following topics - Basic terms, Polarization of Dielectric, Polarization method, Internal Field, Clausius-Mossotti Equation, Types of dielectric, Properties of good Dielectric, and Application of Dielectric.
The Compton effect
Group Name : Red Devils
Member Name & ID
Nusrat Isalm Setu -182-47-736
Md.Nazmul Hasan -182-47-722
Mohammad Imran Bhuiyan -182-47-742
Shafiul Alam -182-47-763
Kazi Hasibul Hasan -182-47-795
*FIRST INTRODUCED The Compton effect was first demonstrated in 1923 by Arthur Holly Compton (for which he received a 1927 Nobel Prize in Physics) Compton's graduate student, Y.H. Woo, later verified the effect.
DEFINITION: • The Compton effect (also called Compton scattering) is the result of a high-energy photon colliding with a target, which releases loosely bound electrons from the outer shell of the atom or molecule .
• The scattered radiation experiences a wavelength shift that cannot be explained in terms of classical wave theory, thus lending support to Einstein's photon theory.
• Probably the most important implication of the effect is that it showed light could not be fully explained according to wave phenomena.
APPLICATIONS:• Compton scattering is of prime importance to radiobiology, as it happens to be the most probable interaction of high energy X rays with atomic nuclei in living beings and is applied in radiation therapy.
• In material physics, Compton scattering can be used to probe the wave function of the electrons in matter in the momentum representation.
• Compton scattering is an important effect in gamma spectroscopy which gives rise to the Compton edge, as it is possible for the gamma rays to scatter out of the detectors used. Compton suppression is used to detect stray scatter gamma rays to counteract this effect.
equation of Compton effect:
THE EXPERIMENT: A graphite target was bombarded with monochromatic x-rays and the wavelength of the scattered radiation was measured with a rotating crystal spectrometer. The intensity was determined by a movable ionization chamber that generated a current proportional to the x-ray intensity. Compton measured the dependence of scattered x-ray intensity on wavelength at three different scattering angles of 45o 90o ,and 135o
The Experimental intensity vs wavelength plots observed by Compton for the three scattering angles show two peaks , one at the wavelength λ of the incident X-rays and the other at a longer wavelength λ’
HOW COMPTON EFFECT WORKS
Transmission electron microscope, high resolution tem and selected area elect...Nano Encryption
The transmission electron microscope is a very powerful tool for material science. A high energy beam of electrons is shone through a very thin sample, and the interactions between the electrons and the atoms can be used to observe features such as the crystal structure and features in the structure like dislocations and grain boundaries. Chemical analysis can also be performed. TEM can be used to study the growth of layers, their composition and defects in semiconductors. High resolution can be used to analyze the quality, shape, size and density of quantum wells, wires and dots.
This presentation covers basics of thermoelectrics with major effects. It also includes applications part of thermoelectrics and some selection criterias for designing TE devices for maximum efficiency.
The following presentation consists of introduction to dielectrics, and includes following topics - Basic terms, Polarization of Dielectric, Polarization method, Internal Field, Clausius-Mossotti Equation, Types of dielectric, Properties of good Dielectric, and Application of Dielectric.
The Compton effect
Group Name : Red Devils
Member Name & ID
Nusrat Isalm Setu -182-47-736
Md.Nazmul Hasan -182-47-722
Mohammad Imran Bhuiyan -182-47-742
Shafiul Alam -182-47-763
Kazi Hasibul Hasan -182-47-795
*FIRST INTRODUCED The Compton effect was first demonstrated in 1923 by Arthur Holly Compton (for which he received a 1927 Nobel Prize in Physics) Compton's graduate student, Y.H. Woo, later verified the effect.
DEFINITION: • The Compton effect (also called Compton scattering) is the result of a high-energy photon colliding with a target, which releases loosely bound electrons from the outer shell of the atom or molecule .
• The scattered radiation experiences a wavelength shift that cannot be explained in terms of classical wave theory, thus lending support to Einstein's photon theory.
• Probably the most important implication of the effect is that it showed light could not be fully explained according to wave phenomena.
APPLICATIONS:• Compton scattering is of prime importance to radiobiology, as it happens to be the most probable interaction of high energy X rays with atomic nuclei in living beings and is applied in radiation therapy.
• In material physics, Compton scattering can be used to probe the wave function of the electrons in matter in the momentum representation.
• Compton scattering is an important effect in gamma spectroscopy which gives rise to the Compton edge, as it is possible for the gamma rays to scatter out of the detectors used. Compton suppression is used to detect stray scatter gamma rays to counteract this effect.
equation of Compton effect:
THE EXPERIMENT: A graphite target was bombarded with monochromatic x-rays and the wavelength of the scattered radiation was measured with a rotating crystal spectrometer. The intensity was determined by a movable ionization chamber that generated a current proportional to the x-ray intensity. Compton measured the dependence of scattered x-ray intensity on wavelength at three different scattering angles of 45o 90o ,and 135o
The Experimental intensity vs wavelength plots observed by Compton for the three scattering angles show two peaks , one at the wavelength λ of the incident X-rays and the other at a longer wavelength λ’
HOW COMPTON EFFECT WORKS
When the energy of the accelerated electrons is higher than a certain threshold value (which depends on the metal anode), a second type of spectrum is obtained superimposed on top of the white radiation. It is called the characteristic radiation and is composed of discrete peaks.
The energy (and wavelength) of the peaks depends solely on the metal used for the target and is due to the ejection of an electron from one of the inner electron shells of the metal atom.
This results in an electron from a higher atomic level dropping to the vacant level with the emission of an X-ray photon characterised by the difference in energy between the two levels.
*Create fun conversations.* Stickers, GIFs, Poptexts & more. Download Bobble Keyboard Now 👇
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*Create fun conversations.* Stickers, GIFs, Poptexts & more. Download Bobble Keyboard Now 👇
MakeMyBobble.in/welcome
*Create fun conversations.* Stickers, GIFs, Poptexts & more. Download Bobble Keyboard Now 👇
MakeMyBobble.in/welcome
*Create fun conversations.* Stickers, GIFs, Poptexts & more. Download Bobble Keyboard Now 👇
MakeMyBobble.in/welcome
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
Removing Uninteresting Bytes in Software FuzzingAftab Hussain
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
zkStudyClub - Reef: Fast Succinct Non-Interactive Zero-Knowledge Regex ProofsAlex Pruden
This paper presents Reef, a system for generating publicly verifiable succinct non-interactive zero-knowledge proofs that a committed document matches or does not match a regular expression. We describe applications such as proving the strength of passwords, the provenance of email despite redactions, the validity of oblivious DNS queries, and the existence of mutations in DNA. Reef supports the Perl Compatible Regular Expression syntax, including wildcards, alternation, ranges, capture groups, Kleene star, negations, and lookarounds. Reef introduces a new type of automata, Skipping Alternating Finite Automata (SAFA), that skips irrelevant parts of a document when producing proofs without undermining soundness, and instantiates SAFA with a lookup argument. Our experimental evaluation confirms that Reef can generate proofs for documents with 32M characters; the proofs are small and cheap to verify (under a second).
Paper: https://eprint.iacr.org/2023/1886
Essentials of Automations: The Art of Triggers and Actions in FMESafe Software
In this second installment of our Essentials of Automations webinar series, we’ll explore the landscape of triggers and actions, guiding you through the nuances of authoring and adapting workspaces for seamless automations. Gain an understanding of the full spectrum of triggers and actions available in FME, empowering you to enhance your workspaces for efficient automation.
We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
Welcome to the first live UiPath Community Day Dubai! Join us for this unique occasion to meet our local and global UiPath Community and leaders. You will get a full view of the MEA region's automation landscape and the AI Powered automation technology capabilities of UiPath. Also, hosted by our local partners Marc Ellis, you will enjoy a half-day packed with industry insights and automation peers networking.
📕 Curious on our agenda? Wait no more!
10:00 Welcome note - UiPath Community in Dubai
Lovely Sinha, UiPath Community Chapter Leader, UiPath MVPx3, Hyper-automation Consultant, First Abu Dhabi Bank
10:20 A UiPath cross-region MEA overview
Ashraf El Zarka, VP and Managing Director MEA, UiPath
10:35: Customer Success Journey
Deepthi Deepak, Head of Intelligent Automation CoE, First Abu Dhabi Bank
11:15 The UiPath approach to GenAI with our three principles: improve accuracy, supercharge productivity, and automate more
Boris Krumrey, Global VP, Automation Innovation, UiPath
12:15 To discover how Marc Ellis leverages tech-driven solutions in recruitment and managed services.
Brendan Lingam, Director of Sales and Business Development, Marc Ellis
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Enhancing Performance with Globus and the Science DMZGlobus
ESnet has led the way in helping national facilities—and many other institutions in the research community—configure Science DMZs and troubleshoot network issues to maximize data transfer performance. In this talk we will present a summary of approaches and tips for getting the most out of your network infrastructure using Globus Connect Server.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
Climate Impact of Software Testing at Nordic Testing DaysKari Kakkonen
My slides at Nordic Testing Days 6.6.2024
Climate impact / sustainability of software testing discussed on the talk. ICT and testing must carry their part of global responsibility to help with the climat warming. We can minimize the carbon footprint but we can also have a carbon handprint, a positive impact on the climate. Quality characteristics can be added with sustainability, and then measured continuously. Test environments can be used less, and in smaller scale and on demand. Test techniques can be used in optimizing or minimizing number of tests. Test automation can be used to speed up testing.
SAP Sapphire 2024 - ASUG301 building better apps with SAP Fiori.pdfPeter Spielvogel
Building better applications for business users with SAP Fiori.
• What is SAP Fiori and why it matters to you
• How a better user experience drives measurable business benefits
• How to get started with SAP Fiori today
• How SAP Fiori elements accelerates application development
• How SAP Build Code includes SAP Fiori tools and other generative artificial intelligence capabilities
• How SAP Fiori paves the way for using AI in SAP apps
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...SOFTTECHHUB
The choice of an operating system plays a pivotal role in shaping our computing experience. For decades, Microsoft's Windows has dominated the market, offering a familiar and widely adopted platform for personal and professional use. However, as technological advancements continue to push the boundaries of innovation, alternative operating systems have emerged, challenging the status quo and offering users a fresh perspective on computing.
One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
1. Dr Ahmad Taufek Abdul Rahman
School of Physics & Material Studies, Faculty of Applied Sciences, Universiti Teknologi MARA Malaysia, Campus of Negeri Sembilan
is defined as an electromagnetic
radiation of shorter wavelength
than UV radiation produced by the
bombardment of atoms by high
energy electrons in x-ray tube.
CHAPTER 6: X-rays
(2 Hours)
discovered by
Wilhelm Konrad Rontgen
in 1895.
1
2. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Learning Outcome:
6.1 X-ray spectra (1 hour)
At the end of this chapter, students should be able to:
Explain with the aid of a diagram, the production of
X-rays from an X-ray tube.
Explain the production of continuous and characteristic
X-ray spectra.
Derive and use the formulae for minimum wavelength for
continuous X-ray spectra,
min
hc
eV
Identify the effects of the variation of current,
accelerating voltage and atomic number of the anode on
the continuous and characteristic X-ray spectra.
2
3. DR.ATAR @ UiTM.NS
PHY310 X-RAY
6.1 X-ray spectra
6.1.1 Properties of x-rays
Its properties are
x-rays travel in a straight lines at the speed of light.
x-rays cannot be deflected by electric or magnetic fields.
(This is convincing evidence that they are uncharged or
neutral particles)
x-rays can be diffracted by the crystal lattice if the spacing
between two consecutive planes of atoms approximately
equal to its wavelength.
x-rays affect photographic film.
x-rays can produce fluorescence and photoelectric
emission.
x-rays penetrate matter. Penetration power is least in the
materials of high density.
3
4. DR.ATAR @ UiTM.NS
PHY310 X-RAY
6.1.2 Production of x-rays
X-rays are produced in an x-ray tube. Figure 6.1 shows a
schematic diagram of an x-ray tube.
Tungsten target
(anode)
Cooling system
X-rays
Evacuated glass
tube
Heated filament
(cathode)
Power supply
High voltage source
for heater
Figure 6.1
An x-ray tube consists of
an evacuated glass tube to allow the electrons strike the
target without collision with gas molecules.
Electrons
4
5. DR.ATAR @ UiTM.NS
PHY310 X-RAY
a heated filament as a cathode and is made from the
material of lower ionization energy.
a target (anode) made from a heavy metal of high
melting point such as tungsten and molybdenum.
a cooling system that is used to prevent the target
(anode) from melting.
a high voltage source that is used to set the anode at a
large 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 emission (is defined as the emission of electrons
from 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.
5
6. DR.ATAR @ UiTM.NS
PHY310 X-RAY
X-rays emission can be considered as the reverse of the
photoelectric effect. In the photoelectric effect, EM radiation
incident on a target causes the emission of electrons but in
an x-ray tube, electrons incident on a target cause the
emission of EM radiation (x-rays).
The radiation produced by the x-ray tube is created by two
completely difference physical mechanisms refer to:
characteristic x-rays
continuous x-rays (called bremsstrahlung in german
which is braking radiation).
Characteristic x-rays
The electrons which bombard the target are very energetic
and are capable of knock out the inner shell electrons from
the target atom, creating the inner shell vacancies.
When these are refilled by electrons from the outer shells,
the electrons 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-rays.
6
7. DR.ATAR @ UiTM.NS
PHY310 X-RAY
The energy of the characteristic x-rays is given by
E hf Ef Ei
(6.1)
Since the energy of characteristic x-rays equal to the difference
of the two energies level, thus its energy is discrete . Then its
frequency and wavelength also discrete.
Figure 6.2 shows the production of characteristic x-rays.
hc
M
L
K
E2 EL EM hf2
2
hc
E1 EK EL hf1
1
High speed electron
vacancy
Figure 6.2
Electron in the shell
Nucleus
7
8. DR.ATAR @ UiTM.NS
PHY310 X-RAY
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
Z 12 ; n 1,2,3,...
En 13.6 eV
2
(6.2)
n
where
En : energy level of n th state (orbit)
Z : atomic number
n : principal quantum number
Table 6.1 shows a shell designation for multielectron atom.
n
Number of electron
1
K
2
2
L
M
8
3
Table 6.1
Shell
18
4
N
32
8
9. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Continuous x-rays (Bremsstrahlung)
Some of high speed electrons which bombard the target
undergo a rapid deceleration. This is braking.
As the electrons suddenly come to rest in the target, a part
or all of their kinetic energies are converted into energy of
EM radiation immediately called Bresmsstrahlung, that is
kinetic energy of the electron
K E energy of EM radiation
1 2
mv hf
2
Note:
(6.3)
These x-rays cover a wide range of wavelengths or frequencies
and its energies are continuous.
The intensity of x-rays depends on
the number of electrons hitting the target i.e. the filament
current.
the voltage 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.
9
10. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Example 1 :
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).
10
11. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Example 1 :
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 : ni 1; nf
By applying the equation of the energy level for multielectron atom,
Z 12
En 13.6 eV
n2
74 12
For K shell, Ei EK 13.6 eV
2
1
7.25 10 eV
For n =, Ef E 0
4
Therefore the minimum energy of the bombarding electron is given
4
by
E Ef Ei
E 0 7.25 10
7.25 10 4 1.60 10 19
11
E 1.16 10 14 J
12. DR.ATAR @ UiTM.NS
PHY310 X-RAY
6.1.3 X-ray spectra
Since there are two types of x-rays are produced in the x-ray
tube, hence the x-ray spectra consist of line spectra (known as
characteristic lines) and continuous spectrum as shown in
Figure 6.3.
Kα
X-ray intensity
The area under the
graph = the total
intensity of x-rays
No x-rays is
produced if
Kγ
min
0 min
Line spectra
(characteristic lines)
Kβ
1 2 3
Figure 6.3
Continuous
spectrum
Wavelength,
12
13. DR.ATAR @ UiTM.NS
PHY310 X-RAY
At low applied voltage across the tube, only a continuous
spectrum of radiation exists. As the applied voltage
increases, groups of sharp peaks superimposed on the
continuous radiation begin to appear. These peaks are lines
spectra (characteristic lines) where it is depend on the target
material.
Characteristic 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 6.1.2).
There are several types of characteristic lines series:
K lines series is defined as the line spectra produced
due to electron transition from outer shell to K shell
vacancy.
K line
Electron transition from L shell (n =2) to
K shell vacancy (n =1)
13
14. DR.ATAR @ UiTM.NS
PHY310 X-RAY
K line
K line
Electron transition from M shell (n =3)
to K shell vacancy (n =1)
Electron transition from N shell (n =4)
to K shell vacancy (n =1)
L lines series is defined as the lines spectra produced
due to electron transition from outer shell to L shell
vacancy.
L line
Electron transition from M shell (n =3)
to L shell vacancy (n =2)
L line
Electron transition from N shell (n =4)
to L shell vacancy (n =2)
L line
Electron transition from O shell (n =5)
to L shell vacancy (n =2)
M lines series is defined as the lines spectra produced
due to electron transition from outer shell to M shell
vacancy.
14
15. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Electron transition from N shell (n =4)
to M shell vacancy (n =3)
M line
Electron transition from O shell (n =5)
to M shell vacancy (n =3)
M line
Electron transition from P shell (n =6) to
M shell vacancy (n =3)
These lines spectra can be illustrated by using the energy level
diagram as shown in Figure 6.4.
Mγ n
EP
6(P shell)
Lγ
M β 5 (O shell)
EO
Mα
Lβ
4 (N shell)
E
M line
N
EM
EL
Kγ
Lα
Kβ
3 (M shell)
2 (L shell)
Kα
EK
Figure 6.4
1 (K shell)
15
16. DR.ATAR @ UiTM.NS
PHY310 X-RAY
These characteristic lines is the property of the target material
i.e. for difference material the wavelengths of the
characteristic lines are different.
Note that the wavelengths of the characteristic lines does not
changes when the applied voltage across x-ray tube changes.
Continuous (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 6.1.2.
According to the x-ray spectra (Figure 6.3), the continuous
spectrum has a minimum wavelength.
The existence of the minimum wavelength is due to the
emission of the most energetic photon where the kinetic
energy of an electron accelerated through the x-ray tube is
completely converted into the photon energy . This happens
when the electron colliding with the target is decelerated and
stopped in a single collision.
16
17. DR.ATAR @ UiTM.NS
PHY310 X-RAY
If the electron is accelerated through a voltage V, the kinetic
energy of the electron is
kinetic energy of the electron
K U electric potential energy
K eV
When the kinetic energy of the electron is completely converted
into the photon energy , thus the minimum wavelength min
of the x-rays is
eV E
hc
eV
min
hc
min
eV
(6.4)
From the eq. (6.4), the minimum wavelength depends on the
applied voltage across the x-ray tube and independent of
target material.
17
18. DR.ATAR @ UiTM.NS
PHY310 X-RAY
6.1.4 Penetrating power (quality) of x-rays
The strength of the x-rays are determined by their penetrating
power.
The penetrating power depends on the wavelength of the xrays where if their wavelength are short then the penetrating
power is high or vice versa.
By using the eq. (6.4) :
hc Penetrating E hc
power
increases
decreases
eV
V
E
P
t
P
X-rays of low penetrating power are called soft x-ray and
those of high penetrating power are called hard x-ray.
18
19. DR.ATAR @ UiTM.NS
PHY310 X-RAY
6.1.5 Factors influence the x-ray spectra
X-rays intensity
Filament current
When
it
is
increased, the
intensity of the
x-ray
spectra
also increased
as shown in
Figure 6.5.
Initial
Final
0 min
Figure 6.5
1 2 3
No change
Wavelength,
19
20. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Applied voltage (p.d.) across x-ray tube
X-rays intensity
When it is
increased, the
intensity of the xray spectra also
increased but the
minimum
wavelength is
decreased.
The wavelengths
of the
characteristic
lines remain
unchanged as
shown in Figure
6.6.
0 f
i
Figure 6.6
1 2 3
No change
Initial
Final
Wavelength,
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21. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Target material
X-rays intensity
When the target
material is
changed with
heavy material
(greater in atomic
number), the
intensity of the xray spectra
increased, the
wavelengths of
the characteristic
lines decreased.
The minimum
wavelength
remains
unchanged as
shown in Figure
6.7.
0
min
Figure 6.7
Initial
Final
'
'
1122'3 3
No change
Wavelength,
21
22. DR.ATAR @ UiTM.NS
PHY310 X-RAY
6.1.6 Difference between x-ray emission spectra
and optical atomic emission spectra
is from the production aspect as shown in Table 6.2.
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 6.2
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23. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Example 2 :
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)
23
24. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Example 2 :
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)
Solution : Z
42
The energy level for K and L shells are
Z 12
En 13.6 eV
n2 2
42 1
E 13.6 eV
K
22862 eV
and
12
42 12
EL 13.6 eV
2
5715 eV
2
24
25. DR.ATAR @ UiTM.NS
Solution :
PHY310 X-RAY
Z 42
The difference between the energy level of K and L shells is
E EK EL
22862 5715
17147 1.60 10 19
E 2.74 10 15 J
Therefore the wavelength corresponds to the E is given by
E
2.74 10 15
hc
6.63 10 3.00 10
34
8
7.26 10 11 m
25
26. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Example 3 :
An x-ray tube has an applied voltage of 40 kV. Calculate
a. 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)
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27. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Example 3 :
An x-ray tube has an applied voltage of 40 kV. Calculate
a. 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)
Solution : V 40 10 3 V
a. The maximum frequency of the x-rays is
hf max eV
6.63 10 f
34
max
1.60 10 19 40 103
f max 9.65 1018 Hz
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28. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Solution : V 40 10 3 V
a. Since the frequency is maximum, thus the minimum wavelength
of x-rays is given by
min
min
c
f max
3.00 108
9.65 1018
3.11 10 11 m
b. The maximum speed of the electron is
1
2
mv max hfmax
2
1
2
9.11 10 31 vmax 6.63 10 34 9.65 1018
2
vmax 1.19 108 m s 1
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29. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Example 4 :
The energy of an electron in the various shells of the nickel atom is
given by Table 6.3.
Shell
Energy (eV) 103
K
8.5
L
1.0
M
0.5
Table 6.3
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)
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30. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Solution :
The difference between the energy level of K and M shells is
E EK EM
8.0 10 1.60 10
8.5 10 3 0.5 10 3
19
3
E 1.28 10 15 J
Therefore the wavelength corresponds to the E is given by
E
1.28 10 15
hc
6.63 10 3.00 10
34
8
1.55 10 10 m
30
31. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Learning Outcome:
6.2 Moseley’s law (½ hour)
At the end of this chapter, students should be able to:
State Moseley’s Law and explain its impact on the
periodic table.
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6.2 Moseley’s law
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 smoothly with that element’s
atomic number Z as shown in Figure 6.8.
8
f K 10
24
Hz
1
2
Zr
16
Cl
8
Figure 6.8
Al
01
8
Y
Cu
Co
Zn
Cr Ni
Ti
Fe
V
K
Si
16
24
32
40
Z
32
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PHY310 X-RAY
From the Figure 6.8, Moseley states that the frequency of K
characteristic lines is proportional to the squared of atomic
number for the target element and could be expressed as
fK
2.48 10
where
15
HzZ 1
2
(6.5)
f K : frequency of the K line;
Z : atomic number of the target element
Eq. (6.5) is known as Moseley’s law.
Moseley’s law is considerable importance in the development
of early quantum theory and the arrangement of modern
periodic table of element (Moseley suggested the
arrangement of the elements according to their atomic number,
Z).
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PHY310 X-RAY
Example 5 :
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)
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PHY310 X-RAY
Example 5 :
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)
9
Solution : K 0.0709 10 m
The frequency of the K line is given by
fK
3.00 108
fK
0.0709 10 9
4.23 1018 Hz
c
K
By applying the Moseley’s law, thus the atomic number for element
is given by
2
15
2.48 10 Z 1
f K 2.48 10 Hz Z 1
4.23 1018
Z 42
15
2
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36. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Learning Outcome:
6.3 X-ray diffraction (½ hour)
At the end of this chapter, students should be able to:
Derive with the aid of a diagram the Bragg’s equation.
Use
2d sin n
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37. DR.ATAR @ UiTM.NS
PHY310 X-RAY
6.3 X-ray diffraction
6.3.1 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 6.9.
C
R
T
i
P
dsin
A
O
air
crystal
B
d
Q
d
dsin
Figure 6.9
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PHY310 X-RAY
From the Figure 6.9, the path difference L between rays RAC
and TBO is given by ΔL PB BQ
ΔL d sin θ d sin θ
ΔL 2d sin θ
(6.6)
The path difference condition for constructive interference
(bright) is
(6.7)
ΔL n ; n 1,2,3,...
By equating the eqs. (6.6) and (6.7), hence
2d sin n
(6.8)
where
d : separationbetween atomicplanes
: glancing angle (thecomplementof incident angle or
diffraction angle)
: wavelength of x - rays
n : diffraction order 1,2,3,...
Eq. (6.8) is known as Bragg’s law and the angle also known
as Bragg angle.
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Note:
The number of diffraction order n depends on the glancing angle
where if is increased then n also increased.
The number of diffraction order n is maximum when the glancing
angle =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
6.3.2 Uses of x-rays
In medicine, x-rays are used to diagnose illnesses and for
treatment.
Soft x-rays of low penetrating power are used for x-rays
photography. X-rays penetrate easily soft tissues such as
the flesh, whereas the bones which are high density and
absorb 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 6.10.
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PHY310 X-RAY
Figure 6.10
Hard x-rays are used in radio therapy for destroying
cancerous cells. It is found that cancerous cells are more
easily damaged by x-rays than stables ones.
In industry : x-rays are used to detect cracks in the interior of
a metal.
X-rays are used to study the structure of crystal by using xray spectrometry since they can be diffracted (Bragg’s law).
40
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PHY310 X-RAY
Example 6 :
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.
Calculate
a. the glancing angle for first order,
b. the maximum number of orders observed.
41
42. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Example 6 :
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.
Calculate
a. the glancing angle for first order,
b. the maximum number of orders observed.
Solution : 0.02 10 9 m; d 3.60 10 10 m
a. Given n 1
By using the Bragg’s law equation, thus
2d sin n
n
sin 1
2d
1 0.02 10 9
sin 1
2 3.60 10 10
1.59
42
43. DR.ATAR @ UiTM.NS
Solution :
PHY310 X-RAY
0.02 10 9 m; d 3.60 10 10 m
b. The number of order is maximum when =90, thus
2d sin n
2d sin 90 nmax
2d
nmax
2 3.60 10 10
0.02 10 9
nmax 36
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PHY310 X-RAY
Intensity
Example 7 :
A
B(25 kV)
5 6 7 8 9 (102 nm)
Figure 6.11
Curves A and B are two x-rays spectra obtained by using two
different voltage. Based on the Figure 6.11 , 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.
44
0
1
2
3
4
45. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Solution :A 2.5 10 11 m; B 5.0 10 11 m; VB 25 10 3 V
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,
hc
(1)
For curve A: A
eVA
hc
For curve B: B
eVB
(2)
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46. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Solution :A 2.5 10 11 m; B 5.0 10 11 m; VB
b.
By dividing the eqs. (2) and (1) thus
20 103 V
hc
eV
B B
A hc
eV
A
B VA
VA
5.0 10 11
11
A VB
2.5 10
25 10 3
VA 50 10 3 V
By substituting the value of VA into the eq. (1) :
2.5 10
11
h 3.00 10 8
1.60 10 19 50 10 3
h 6.67 10 34 J s
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47. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Exercise 6.1 :
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. Calculate
a. 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 xrays generated.
ANS. : 10 keV; 1.231011 m; 1.601015 J, 1.241010 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.
47
ANS. : 0.012 A; 1.33108 m s1
48. DR.ATAR @ UiTM.NS
PHY310 X-RAY
Exercise 6.1 :
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 xrays 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, 3rd edition, James S. Walker, Q54, p.1069)
ANS. : 1.291014 J; 80.6103 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. : 5.591010 m
48