48X-rays

📚
X-RAYS
▢ Introduction:

Table 1: Basic Facts

Fact
Answer
Discovered by
Roentgen
Production condition
Fast electrons strike suitable target of high atomic weight and high melting point
Nature
Electromagnetic waves
Wavelength range
\(100Å\) to \(0.1Å\)
Frequency range
\(10^{16}\ Hz\) to \(10^{19}\ Hz\)
Production efficiency
< 1%
Position in EM spectrum
Between gamma rays and ultraviolet rays
▢ Properties of X-Rays:

Table 1: Properties

Property
Answer
Visibility
Invisible
Path
Travel in straight lines
Speed
Speed of light \((c)\)
Wave properties
Reflection, refraction, interference, diffraction, polarisation
Fluorescence
Produce illumination on fluorescent materials
Photographic plate
Affect photographic plate
Penetration
Pass through flesh and blood but not through bones
Effects
Photoelectric effect and Compton effect
RADAR
Cannot be used because not reflected by target
Best absorber
Lead \((Pb)\)
Ionization
Ionise gases through which they pass
Prism / lens
Not deviated by prisms or lenses
Electric and magnetic field
Not deflected
▢ Production of X-Rays:
❖ Principle: High-speed electrons are suddenly decelerated after striking heavy metal target

Table 1: X-Ray Tubes

Tube
Also called
Gas filled tube
Roentgen X-ray tube
Modern Coolidge tube
Hot filament tube

Table 2: Target Requirements

Requirement
Reason / Example
High atomic number
More efficient X-ray production
High melting point
Withstands heat
Examples
Tungsten, platinum, molybdenum
❖ Atomic Phenomenon: Production of X-rays is atomic phenomenon
❖ Gamma Ray Difference: Production of gamma rays is nuclear phenomenon
▢ Quality and Intensity Control:
❖ Quality: Penetrating power of X-rays
❖ Intensity: Number of X-ray photons produced from target

Table 1: Control of X-Rays

Quantity
Depends on
Quality / penetrating power
Potential difference between filament/cathode and target
Energy of X-rays
Potential difference across filament and target
Intensity
Number of electrons striking target
Number of electrons striking target
Filament temperature and filament current
Intensity relation
\(I*{X-ray}\propto\) filament current
Common tube voltage
About \(10kV\)
▢ Hard and Soft X-Rays:

Table 1: Hard X-Rays vs Soft X-Rays

Feature
Hard X-rays
Soft X-rays
Wavelength
\(0.1Å-10Å\)
\(10Å-100Å\)
Frequency
High
Low
Energy
High
Low
Penetrating power
High
Low
▢ X-Ray Spectrum:
❖ Types:
  • •
    Continuous X-ray spectrum
  • •
    Characteristic X-ray spectrum
▢ Continuous X-Ray Spectrum:
❖ Origin: Produced due to retardation/deceleration of high-speed electrons in strong electric field of heavy nucleus
❖ Bremsstrahlung: Continuous X-rays are produced when bombarding electrons decelerate near nucleus
❖ Maximum Energy Case: When electron loses all kinetic energy in one collision, maximum energy photon is emitted

Table 1: Continuous X-Ray Formulae

Quantity
Formula
Maximum photon energy
\(h\nu*{max}=eV\)
Maximum frequency
\(\nu*{max}=\frac{eV}{h}\)
Minimum wavelength
\(\lambda*{min}=\frac{hc}{eV}\)
Minimum wavelength in Å
\(\lambda*{min}=\frac{12400}{V}Å\)
Relation
\(\lambda*{min}\propto\frac{1}{V}\)
❖ Duane-Hunt Law: Minimum / limiting wavelength is inversely proportional to applied voltage
❖ Important Points:
  • •
    Continuous X-ray spectrum is independent of nature of target and atomic number
  • •
    Wavelength and frequency of continuous spectrum depend on applied potential difference
  • •
    X-ray beam from tube has all wavelengths greater than a certain minimum wavelength
▢ Characteristic X-Ray Spectrum:
❖ Origin: Produced when high-energy electrons knock out inner-shell electrons from K, L or M shells of target atom
❖ Cause: Electrons from higher shells jump to lower vacant shells and emit characteristic X-rays
❖ Depends On:
  • •
    Atomic number of target
  • •
    Nature of target material
❖ Independent Of: Accelerating potential difference, after required threshold is reached
❖ Energy Formula: \(\Delta E=\frac{hc}{\lambda}\)
❖ Wavelength Formula: \(\lambda=\frac{hc}{\Delta E}\)

Table 1: Characteristic X-Ray Series

Series
Final shell
Transition
K-series
\(n=1\)
Higher shells \((n=2,3,4,5,...)\) to K-shell
L-series
\(n=2\)
Higher shells \((n=3,4,5,...)\) to L-shell
M-series
\(n=3\)
Higher shells \((n=4,5,6,...)\) to M-shell

Table 2: K-Series Lines

Line
Transition
\(K*\alpha\)
\(n=2\to n=1\)
\(K*\beta\)
\(n=3\to n=1\)
\(K*\gamma\)
\(n=4\to n=1\)

Table 3: L-Series Lines

Line
Transition
\(L*\alpha\)
\(n=3\to n=2\)
\(L*\beta\)
\(n=4\to n=2\)
\(L*\gamma\)
\(n=5\to n=2\)
▢ K-Alpha Line:

Table 1: \(K*\alpha\) Wavelength

Quantity
Formula
General
\(\frac{1}{\lambda*{K*\alpha}}=R(Z-1)^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)\)
For \(n_1=1,n_2=2\)
\(\frac{1}{\lambda*{K*\alpha}}=R(Z-1)^2\left(1-\frac{1}{4}\right)\)
Result
\(\frac{1}{\lambda*{K*\alpha}}=\frac{3R(Z-1)^2}{4}\)
Wavelength
\(\lambda*{K*\alpha}=\frac{4}{3R(Z-1)^2}\)
▢ Moseley's Law:
❖ Statement: Square root of frequency of characteristic X-ray line is proportional to atomic number
❖ _*table:
    ❖ Important Point: Position of potassium and argon in periodic table was interchanged due to study of Moseley's law
    ▢ Diffraction of X-Rays and Bragg's Law:
    ❖ Condition: X-ray beam of wavelength \(\lambda\) incident on crystal with interplanar spacing \(d\) at glancing angle \(\theta\)
    ❖ _*table:
      ❖ NaCl Example:
      ◉ Formula: \(d=\frac{a_0}{\sqrt5}\)
      ◉ Given: \(a_0=5.63Å\)
      ◉ Result: \(d=2.53Å\)
      ▢ Absorption of X-Rays:

      Table 1: Absorption Formulae

      Quantity
      Formula / Meaning
      Intensity after thickness \(x\)
      \(I=I_0e^{-\mu x}\)
      Absorption coefficient
      \(\mu\)
      Half-value thickness
      \(x*{1/2}\)
      Coefficient relation
      \(\mu=\frac{0.693}{x*{1/2}}\)
      Dependence
      \(\mu\) depends on material and wavelength
      Approx relation
      \(\mu\propto Z^4\lambda^3\)
      Highest absorber
      Lead \((Pb)\)
      Use of lead
      Radiation shielding
      ▢ Uses of X-Rays:
      ❖ _*table:
        ▢ X-Rays vs Photoelectric Effect:

        Table 1: Inverse Phenomena

        Process
        Energy conversion
        Photoelectric effect
        Electromagnetic wave energy ejects electron
        X-ray production
        Kinetic energy of electrons produces electromagnetic waves
        ❖ Statement: Production of X-rays is inverse phenomenon of photoelectric effect
        ▢ Read and Digest:

        Table 1: Important Points

        Fact
        Answer
        Target material
        High melting point and high atomic number
        Common targets
        Tungsten, platinum, molybdenum
        Hydrogen atom
        Cannot emit X-rays because energy levels are too close
        X-ray intensity
        Depends on number of electrons striking target
        Number of electrons striking target
        Depends on filament temperature and current
        X-ray energy and penetrating power
        Depend on potential difference across filament and target
        Tube voltage
        About \(10kV\)
        EM spectrum position
        Between gamma rays and UV rays
        Increasing potential difference
        Minimum wavelength decreases
        Hard X-rays
        High energy, high frequency, low wavelength
        Soft X-rays
        Low energy, low frequency, high wavelength
        Intensity measurement
        Ionisation chamber
        Cut-off wavelength
        Depends on voltage applied to tube
        K-electron capture
        Accompanied by characteristic X-ray emission
        Radiotherapy
        X-rays used to treat cancer
        Continuous X-rays
        Due to deceleration of bombarding electrons in field of heavy nucleus
        Characteristic X-rays
        Due to jumps of electrons from higher shells to lower vacant shells
        X-ray beam from tube
        Has all wavelengths larger than minimum wavelength
        Bragg's law
        No solution if \(\lambda>2d\)
        ▢ High-Yield Recall:

        Table 1: X-Rays One-Liners

        Fact
        Answer
        X-rays discovered by
        Roentgen
        Nature
        Electromagnetic waves
        Wavelength range
        \(100Å\) to \(0.1Å\)
        Frequency range
        \(10^{16}\) to \(10^{19}Hz\)
        Efficiency
        < 1%
        Best absorber
        Lead
        Target
        High Z and high melting point
        Quality
        Penetrating power
        Quality depends on
        Potential difference
        Intensity depends on
        Filament current
        Hard X-rays
        High frequency, high energy, low wavelength
        Soft X-rays
        Low frequency, low energy, high wavelength
        X-ray spectrum
        Continuous and characteristic
        Continuous X-rays
        Due to deceleration of high-speed electrons
        Characteristic X-rays
        Due to electronic transition to inner vacant shell
        Maximum frequency
        \(\nu*{max}=\frac{eV}{h}\)
        Minimum wavelength
        \(\lambda*{min}=\frac{hc}{eV}=\frac{12400}{V}Å\)
        Duane-Hunt law
        \(\lambda*{min}\propto\frac{1}{V}\)
        K-series
        Transitions to \(n=1\)
        L-series
        Transitions to \(n=2\)
        \(K*\alpha\)
        \(n=2\to1\)
        \(K*\beta\)
        \(n=3\to1\)
        Moseley's law
        \(\sqrt{\nu}=a(Z-b)\)
        Bragg's law
        \(2d\sin\theta=n\lambda\)
        Maximum Bragg wavelength
        \(\lambda*{max}=2d\)
        X-ray absorption
        \(I=I_0e^{-\mu x}\)
        Absorption coefficient
        \(\mu=\frac{0.693}{x*{1/2}}\)
        Radiotherapy
        Cancer treatment
        X-ray crystallography
        3D structure of proteins
        Q1.
        X-ray can penetrate muscles but not bones because bones have:
        📅CEE Nursing 2024
        Q2.
        Bragg's law has no solution if:
        📅CEE Nursing 2024
        Q3.
        Which of the following is correct about X-rays?
        📅CEE MBBS 2024a
        Q4.
        Bragg's law has no solution if:
        📅CEE MBBS 2024a
        Q5.
        Hard X-rays differ from soft X-rays in having:
        📅CEE MBBS 2023
        Q6.
        Characteristics X-ray are produced due to:
        📅CEE BDS 2024
        Q7.
        Hard X-ray depends on:
        📅CEE BDS 2023
        Q8.
        Characteristics X-ray depends upon:
        📅CEE BDS 2023
        Q9.
        Cut off wavelength of X-ray depends upon:
        📅CEE BDS 2021
        Q10.
        Which electromagnetic radiation is commonly used to determine the internal arrangement of atoms in crystals?
        📅IOM 2013
        Q11.
        An X-ray tube operates at \(20\,\mathrm{kV}\). Neglecting relativistic corrections, what is the approximate maximum speed of electrons striking the target?
        📅MOE 2013
        Q12.
        An incident X-ray photon has wavelength \(0.5\,\mathrm{\AA}\) and is scattered through \(72^\circ\). What is the energy of the **incident** photon?
        📅MOE 2068
        Q13.
        The shortest wavelength of X-ray in continuous spectrum from an X-ray tube depends on
        📅MOE 2068
        Q14.
        An X-ray has a wavelength of 0.01Å. Its momentum in kg.m/s is
        📅MOE 2010
        Q15.
        Planck's constant is given as 6.6×\(10^{-34}\) Js. The minimum wavelength of X-rays emitted by X-rays tube operating at 30 KV in Å will be nearly
        📅MOE 2009
        Q16.
        X-rays of wavelength 3Å have frequency of
        📅KU 2010
        Q17.
        To obtain X-rays with a shorter minimum wavelength from the same X-ray tube, one should:
        📅BP 2010
        Q18.
        Why does an isolated hydrogen atom not produce the usual high-energy characteristic X-ray lines of heavy atoms?
        📅BP 2013
        Q19.
        An X-ray tube is operating at 15KV. The lower limit of wavelength of X-rays produced is
        📅I.E. 2013
        Q20.
        A photon has energy \(1\,\mathrm{eV}\). What is its wavelength?
        📅I.E. 2013
        Q21.
        An electromagnetic wave in vacuum has frequency \(100\,\mathrm{Hz}\). What is its wavelength?
        📅I.E. 2011
        Q22.
        A metal surface has a work function of 4eV. The maximum wavelength of light which can eject the electrons from the surface is
        📅I.E. 2012
        Q23.
        A radio station broadcasts at a wavelength of \(30\,\mathrm m\). What is the frequency?
        📅I.E. 2012
        Q24.
        The hardness (penetrating ability) of X-rays from an X-ray tube can be increased by increasing:
        📅BP 2014
        Q25.
        An X-ray tube operates at \(50\,\mathrm{kV}\) and produces \(740\,\mathrm W\) of heat at its target. If 0.5% of incident electron energy becomes X-rays, approximately how many electrons hit the target each second?
        📅MOE 2014
        Q26.
        If \(h\) is Planck’s constant, \(c\) is the speed of light, \(e\) is the elementary charge and \(V\) is the X-ray tube accelerating voltage, the **minimum** emitted X-ray wavelength is:
        📅Bangladesh 09
        Q27.
        The wavelength of the most energetic X-rays emitted when a metal target is bombarded by 40KV supply is
        📅MOE 2065
        Q28.
        Characteristic X-ray emission from atoms involves energy transitions of:
        📅MOE 2062
        Q29.
        What should be the nature of anticathode in an X-ray tube?
        📅MOE 2061
        Q30.
        The voltage applied to an X-ray is 5000V. What is the minimum wavelength of X-ray produced
        📅YE-05
        Q31.
        When a beam of accelerated electrons hit a target, a continuous X-ray spectrum is emitted from the target. Which one of the following wavelengths is absent in the X-ray spectrum if the X-ray tube is operated at 40,000 V?
        📅BPKIHS-07
        Q32.
        Hard X-rays have a shorter _____ than soft X-rays.
        📅BPKIHS-09
        Q33.
        Why do bones appear relatively white in a conventional X-ray radiograph?
        📅BPKIHS-04
        Q34.
        The X-ray tube is operated at 50 kV. The minimum wavelength is about
        📅BPKIHS-06
        Q35.
        In obtaining an X-ray photograph of hand we use principle of
        📅BPKIHS-94
        Q36.
        When cathode rays strike a metal target of high melting point with a very high velocity then which of the following is produced?
        Q37.
        As the potential difference applied to X-ray tube is increased, as a result in the emitted radiation
        Q38.
        A LASER produces
        Q39.
        Penetrating power of X-ray can be increased by
        Q40.
        For lattice planes separated by \(d=15\,\mathrm{\AA}\), what is the maximum wavelength that can satisfy first-order Bragg reflection?
        Q41.
        For which of the following voltage will the wavelength of emitted X-rays will be minimum?
        Q42.
        The potential difference between the cathode and anticathode in a Coolidge tube is 120 kV. The maximum frequency of X-rays emitted by it will be
        Q43.
        In an X-ray tube, if the electrons are accelerated through 140kV, then anode current obtained is 30mA. If the whole energy of electrons is converted into heat, then the rate of production of heat (in calories/sec) at anode will be
        Q44.
        When X-rays of wavelength 1 Å passes through a gold foil of thickness 2.303 mm, then their intensity reduces to half. The coefficient of absorption for gold (in \(mm^{-1}\)) will be
        Q45.
        An X-ray tube operates at \(40\,\mathrm{kV}\) and \(20\,\mathrm{mA}\); 2% of electrical input becomes X-rays. What is the maximum energy of **one emitted photon**?
        Q46.
        Initially, 50% of an X-ray beam passes through \(0.3\,\mathrm{mm}\) of aluminium. If accelerating voltage is increased while the filter is unchanged, approximately what happens to the transmitted fraction?
        Q47.
        The frequency of the characteristic \(K_\alpha\) X-ray line of an element with atomic number \(31\) is \(f\). Using Moseley’s approximation \(f\propto(Z-1)^2\), what is the frequency for atomic number \(51\)?
        Q48.
        X-rays are:
        📅KU 2017