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.
        The internal structure of crystal can be studied by
        [IOM 2013]
        📅IOM 2013
        Q2.
        An X-ray tube is operated at 20KV. The maximum speed of electrons striking the anticathode will be
        [MOE 2013]
        📅MOE 2013
        Q3.
        X-rays of wavelength 0.5Å are scattered by a target. What will be the energy of incident X-rays if these are scattered at an angle of 72°
        [MOE 2068]
        📅MOE 2068
        Q4.
        The shortest wavelength of X-ray in continuous spectrum from an X-ray tube depends on
        [MOE 2068]
        📅MOE 2068
        Q5.
        An X-ray has a wavelength of 0.01Å. Its momentum in kg.m/s is
        [MOE 2010]
        📅MOE 2010
        Q6.
        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]
        📅MOE 2009
        Q7.
        X-rays of wavelength 3Å have frequency of
        [KU 2010]
        📅KU 2010
        Q8.
        The minimum wavelength of X-rays can be obtained by
        [BP 2010]
        📅BP 2010
        Q9.
        Hydrogen atom cannot produce X-ray because
        [BP 2013]
        📅BP 2013
        Q10.
        An X-ray tube is operating at 15KV. The lower limit of wavelength of X-rays produced is
        [I.E. 2013]
        📅I.E. 2013
        Q11.
        Find out the wavelength from the following figure where energy = 1eV
        [I.E. 2013]
        📅I.E. 2013
        Q12.
        A light wave has a frequency of 100Hz. The wavelength of the wave is:
        [I.E. 2011]
        📅I.E. 2011
        Q13.
        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]
        📅I.E. 2012
        Q14.
        A radio station has a band 30m. The frequency of electromagnetic waves from this station will be
        [I.E. 2012]
        📅I.E. 2012
        Q15.
        Hardness of X-ray can be increased by increasing:
        [BP 2014]
        📅BP 2014
        Q16.
        An X-ray tube operated at 50 KV produces heat at the target at the rate of 740 watt. If 0.5% energy of incident electron is converted into X-rays, then the number of electrons striking the target per second will be
        [MOE 2014]
        📅MOE 2014
        Q17.
        If 'h' is Planck's constant, 'c' is velocity of light, 'e' is electronic charge and 'V' is the accelerating potential then maximum wavelength of emitted X-ray photon is given by
        [Bangladesh 09]
        📅Bangladesh 09
        Q18.
        The wavelength of the most energetic X-rays emitted when a metal target is bombarded by 40KV supply is
        [MOE 2065]
        📅MOE 2065
        Q19.
        X-rays are produced by energy change in:
        [MOE 2062]
        📅MOE 2062
        Q20.
        What should be the nature of anticathode in an X-ray tube?
        [MOE 2061]
        📅MOE 2061
        Q21.
        The voltage applied to an X-ray is 5000V. What is the minimum wavelength of X-ray produced
        [YE-05]
        📅YE-05
        Q22.
        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]
        📅BPKIHS-07
        Q23.
        Hard and Soft X-ray depends on
        [BPKIHS-09]
        📅BPKIHS-09
        Q24.
        X-ray can't penetrate bone because bones have
        [BPKIHS-04]
        📅BPKIHS-04
        Q25.
        The X-ray tube is operated at 50 kV. The minimum wavelength is about
        [BPKIHS-06]
        📅BPKIHS-06
        Q26.
        In obtaining an X-ray photograph of hand we use principle of
        [BPKIHS-94]
        📅BPKIHS-94
        Q27.
        When cathode rays strike a metal target of high melting point with a very high velocity then which of the following is produced?
        Q28.
        As the potential difference applied to X-ray tube is increased, as a result in the emitted radiation
        Q29.
        A LASER produces
        Q30.
        Penetrating power of X-ray can be increased by
        Q31.
        The maximum distance between inter-atomic lattice planes is 15 Å. The maximum wavelength of X-rays which are diffracted by the crystal will be
        Q32.
        For which of the following voltage will the wavelength of emitted X-rays will be minimum?
        Q33.
        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
        Q34.
        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
        Q35.
        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
        Q36.
        An X-ray tube is operated at an accelerating potential of 40kV and the current in the tube is 20mA. Only 2% of the total energy given is converted into X-rays. The maximum energy of emitted radiations will be
        Q37.
        50% of X-rays obtained from a Coolidge tube pass through 0.3 mm thick aluminum foil. If the p.d between the target and the cathode is increased, then the fraction of X-rays passing through the same foil will be
        Q38.
        If the frequency of Kα X-ray emitted from the element with atomic number 31 is ν, then the frequency of Kα X-ray emitted from the element with atomic number 51 would be
        Q39.
        X-rays are:
        [KU 2017]
        📅KU 2017