47Photoelectric effect

📚
PHOTOELECTRIC EFFECT
▢ Photon:
❖ Definition: Photon = packet / quantum of radiation energy moving with speed of light

Table 1: Photon Formulae

Quantity
Formula
Energy
\(E=h\nu=\frac{hc}{\lambda}\)
Relativistic energy
\(E=mc^2\)
Dynamic mass
\(m=\frac{E}{c^2}=\frac{h\nu}{c^2}=\frac{h}{c\lambda}\)
Momentum
\(p=mc=\frac{h\nu}{c}=\frac{h}{\lambda}=\frac{E}{c}\)
Rest mass
\(m_0=0\)
Charge
0
❖ Important Points:
  • •
    Photon travels in straight line with speed \(c\)
  • •
    Photon is electrically neutral
  • •
    Photon is not deflected by electric and magnetic fields
  • •
    Photon frequency does not change in different media
  • •
    Photon velocity changes in medium due to change in wavelength
  • •
    Energy of photon is purely kinetic
▢ Photoelectric Effect:
❖ Definition: Emission of electrons from metal surface when light of suitable frequency falls on it
❖ Photoelectron: Electron emitted from metal surface by incident photon
❖ Nature: Instantaneous phenomenon
❖ Time Lag: Less than \(10^{-9}\ s\)
❖ Energy Conversion: Light energy → electrical energy
❖ Based On: Conservation of energy
❖ One-to-One Interaction: One photon interacts with one electron and may eject one photoelectron

Table 1: Photoelectric Effect Facts

Fact
Answer
Best metal
Cesium \((Cs)\)
Suitable metals
Low work function metals / alkali metals
UV rays
Can cause photoelectric effect from many metals
Visible light
Can cause photoelectric effect mainly from alkali metals
Infrared radiation
Cannot cause photoelectric effect from ordinary surfaces
Threshold frequency of alkali metals
Visible range
Threshold frequency of zinc
UV range
Efficiency
Less than 1%
Reverse phenomenon
X-ray production
▢ Work Function:
❖ Symbol: \(\phi\) or \(W_0\)
❖ Definition: Minimum energy required by an electron to just escape from metal surface

Table 1: Work Function Formulae

Quantity
Formula
Work function
\(\phi=h\nu_0\)
Using threshold wavelength
\(\phi=\frac{hc}{\lambda_0}\)
Threshold frequency
\(\nu_0=\frac{\phi}{h}\)
Threshold wavelength
\(\lambda_0=\frac{hc}{\phi}\)
❖ Alkali Metal Trend:
  • •
    Atomic number increases → work function decreases
  • •
    Temperature increases → work function decreases
❖ Condition for Emission:
  • •
    \(h\nu\geq\phi\)
  • •
    \(\nu\geq\nu_0\)
  • •
    \(\lambda\leq\lambda_0\)
▢ Laws of Photoelectric Emission:
❖ **table:
    ❖ Intensity Relation:
      ◈ **type: bullet
    1. Intensity \(I=\frac{Energy}{Area\times time}=\frac{Power}{Area}\)
    2. Intensity \(\propto\) photons falling per second
    3. Intensity \(\propto\) electrons emitted per second
    4. Intensity \(\propto\) photoelectric current
    5. Intensity \(\propto\frac{1}{d^2}\)
    ▢ Einstein Photoelectric Equation:
    ❖ Energy Distribution: Photon energy is used to overcome work function and remaining energy appears as maximum kinetic energy of photoelectron
    ❖ **table:
      ❖ Graph:
        ◈ **type: bullet
      1. Graph of \(K*{max}\) vs \(\nu\) is straight line
      2. Slope of \(K*{max}\) vs \(\nu\) graph = \(h\)
      3. Intercept on frequency axis = \(\nu_0\)
      ▢ Stopping Potential:
      ❖ Symbol: \(V_0\)
      ❖ Definition: Minimum negative potential applied to anode of photocell for which photoelectric current becomes zero
      ❖ _*table:
        ❖ Important Points:
        • •
          Stopping potential is independent of intensity
        • •
          Stopping potential increases with frequency
        • •
          Stopping potential depends on nature of photosensitive surface
        • •
          Stopping potential becomes zero at threshold frequency
        ▢ Effect of Frequency and Wavelength:
        ❖ _*table:
          ▢ Photocell:
          ❖ Definition: Device based on photoelectric effect that converts light energy into electrical energy
          ❖ Current Relation: Photocurrent is directly proportional to intensity of incident light
          ❖ Uses:
          • •
            Automatic control system
          • •
            Light meter
          • •
            Sound reproduction
          • •
            Burglar alarm
          • •
            Counting objects
          ▢ de Broglie Matter Waves:
          ❖ Definition: Wave associated with moving material particle

          Table 1: de Broglie Formulae

          Condition
          Formula
          General wavelength
          \(\lambda=\frac{h}{p}=\frac{h}{mv}\)
          Kinetic energy \(K\)
          \(\lambda=\frac{h}{\sqrt{2mK}}\)
          Charged particle accelerated through p.d. \(V\)
          \(\lambda=\frac{h}{\sqrt{2mqV}}\)
          Thermal particle at temperature \(T\)
          \(\lambda=\frac{h}{\sqrt{2mkT}}\)
          Energy of photon in eV
          \(E=\frac{12400}{\lambda}\ eV\), where \(\lambda\) in Å
          ❖ Shortcuts:
          ◉ _*table:
            ❖ Important Points:
            • •
              Matter waves are associated with all moving particles
            • •
              de Broglie wavelength is independent of charge
            • •
              de Broglie wavelength depends on mass, velocity, momentum and frequency
            • •
              For same kinetic energy: smaller mass → larger wavelength
            • •
              According to de Broglie, wave nature exists for both light and material particles
            ▢ Particle Constants:
            ❖ _*table:
              ▢ Heisenberg Uncertainty Principle:
              ❖ Statement: It is impossible to measure two canonically conjugate quantities exactly and simultaneously

              Table 1: Uncertainty Relations

              Pair
              Relation
              Energy-time
              \(\Delta E\Delta t\geq\frac{h}{2\pi}\)
              Position-momentum
              \(\Delta x\Delta p\geq\frac{h}{2\pi}\)
              Angular momentum-angular displacement
              \(\Delta L\Delta\theta\geq h\)
              ❖ Importance:
              • •
                Applicable to microscopic particles
              • •
                Against Bohr's theory
              • •
                Explains non-existence of electron inside nucleus
              • •
                Explains finite width of spectral lines
              • •
                Supports probability theory in quantum mechanics
              ▢ Compton Effect:
              ❖ Definition: Increase in wavelength of photon after collision with free electron
              ❖ Usually Associated With: X-rays
              ❖ _*table:
                ❖ Important Points:
                • •
                  Scattered photon wavelength is greater than incident photon wavelength
                • •
                  Compton shift is independent of incident wavelength
                • •
                  Compton shift depends on angle of scattering
                • •
                  Shows particle nature of radiation
                ▢ X-rays and Photoelectric Effect:
                ❖ Relation: Production of X-rays is inverse of photoelectric effect

                Table 1: Comparison

                Process
                Energy conversion
                Photoelectric effect
                Photon energy → kinetic energy of electron
                X-ray production
                Kinetic energy of electron → photon energy
                ▢ Wave Theory Limitations:
                ❖ Photoelectric Effect Cannot Be Explained By Classical Wave Theory Because:
                • •
                  Photoelectric emission is instantaneous
                • •
                  Existence of threshold frequency
                • •
                  Maximum kinetic energy depends on frequency, not intensity
                • •
                  Photoelectric current depends on intensity
                • •
                  Stopping potential depends on frequency
                • •
                  One photon interacts with one electron
                ▢ Read and Digest:

                Table 1: Important Points

                Fact
                Answer
                Photoelectric effect discovered by
                Hertz
                Photoelectric effect explained by
                Einstein
                Photoelectric effect verified by
                Millikan
                Photon rest mass
                Zero
                Photon dynamic mass
                \(m=\frac{h}{c\lambda}\)
                Photon momentum
                \(p=\frac{h}{\lambda}\)
                Planck constant dimension
                Same as angular momentum
                Photoelectric effect
                Based on conservation of energy
                Number of photoelectrons
                Depends on intensity of incident light
                Maximum kinetic energy
                Depends on frequency and nature of surface
                Stopping potential
                Independent of intensity
                Stopping potential
                Directly related to frequency
                Compton shift
                Depends on scattering angle
                Matter waves
                Associated with all moving particles
                Particle nature of light
                Established by photoelectric effect
                Wave nature of matter
                Established by de Broglie hypothesis
                Photons exert
                Pressure
                Order of \(e/m\)
                Electron > proton > alpha particle
                If intensity increases
                Photocurrent increases
                If frequency increases
                Maximum kinetic energy increases
                If wavelength increases
                Maximum kinetic energy decreases
                ▢ Objective Answer Key:
                ❖ _*table:
                  ▢ High-Yield Recall:
                  ❖ **table:
                    Q1.
                    If a photon has 100 eV energy then its frequency is
                    📅TOM 2009
                    Q2.
                    Planck's constant has the dimension of
                    📅MOE 2013
                    Q3.
                    If a pd of 1V is applied across an electron, the energy gained by it will be
                    📅MOE 2012
                    Q4.
                    Electron, proton, neutron and alpha particle have the same K.E. Which has the highest de-Broglie wavelength?
                    📅MOE 2012 & 2068
                    Q5.
                    A metal (work function 3.31 eV) is illuminated by light of wavelength 5×10-7 m. The threshold frequency is:
                    📅MOE 2010
                    Q6.
                    Light (λ=400nm) on metal (threshold λ=600nm) produces current I. If λ is doubled, photoelectric current will be:
                    📅MOE 2068
                    Q7.
                    If K.E. of a particle increases by four times, de-Broglie wavelength becomes:
                    📅MOE 2010
                    Q8.
                    The de-Broglie wavelength of electron is 1.224 Å. The energy of electron in eV is:
                    📅MOE 2010
                    Q9.
                    An electron (mass 'm', charge 'e') is accelerated from rest through pd. 'V' volts. Its speed will be:
                    Q10.
                    In photoelectric effect, the number of ejected electrons per second depends on:
                    📅KU 2012
                    Q11.
                    The wavelength associated with an electron (mass m, velocity v) is:
                    📅KU 2011
                    Q12.
                    Work function = 2 eV. Velocity of emitted electron when λ=230 nm light is incident?
                    📅KU 2010
                    Q13.
                    Which wavelength falls under visible light?
                    Q14.
                    Which has frequency 6 × 1015 Hz?
                    📅BP 2012
                    Q15.
                    Two photons traveling opposite directions have relative velocity:
                    📅I.E. 2009
                    Q16.
                    Photoelectric effect is explained by:
                    📅I.E. 2009
                    Q17.
                    An α-particle and proton accelerated through same potential. Ratio of final velocities:
                    📅I.E. 2011
                    Q18.
                    Particle nature of light is shown by:
                    📅TOM 2014
                    Q19.
                    Light (1.5× threshold frequency) on material. If frequency is halved and intensity doubled, photocurrent becomes:
                    📅MOE 2014
                    Q20.
                    What will be the maximum velocity of photoelectrons ejected from a metal (work function 1eV) when light of wavelength 3000Å falls on it?
                    📅MOE 2014
                    Q21.
                    Which phenomenon does NOT support the wave theory of light?
                    📅BP 2014
                    Q22.
                    If threshold frequency increases, what happens to the K.E. of photoelectrons?
                    📅BP 2014
                    Q23.
                    Value of Planck’s constant (h) is:
                    📅BP 2014
                    Q24.
                    Uncertainty in proton position is 6×10-8 m. Minimum uncertainty in speed is:
                    📅BP 2014
                    Q25.
                    Ratio of de Broglie wavelengths of proton and α-particle with same K.E.:
                    📅BP 2014
                    Q26.
                    Work function = 3.3 eV. Threshold frequency is:
                    📅MOE 066
                    Q27.
                    UV photon (work function = 2 eV) produces photoelectron with 2 eV energy. Photon wavelength is:
                    📅MOE 2065
                    Q28.
                    Photoelectric effect conserves:
                    📅MOE 2063
                    Q29.
                    Light (frequency 3ν0) on material. If frequency is halved and intensity doubled, photocurrent becomes:
                    Q30.
                    Behind cutoff voltage, photoelectron emission is proportional to:
                    📅I.E. 06
                    Q31.
                    Photoelectrons from a monochromatic beam have:
                    📅BPKIHS-08
                    Q32.
                    Increasing light intensity affects:
                    📅BPKIHS 02
                    Q33.
                    When frequency increases:
                    📅BPKIHS 02
                    Q34.
                    Photocell current is:
                    📅BPKIHS-04
                    Q35.
                    UV radiation (6.2 eV) on aluminum (φ = 4.2 eV). K.E.max is:
                    📅BPKIHS 05
                    Q36.
                    Photoelectric effect occurs if incident light frequency is:
                    📅BPKIHS 05
                    Q37.
                    Photoelectric effect proves the existence of:
                    Q38.
                    Number of photons for fixed energy varies:
                    Q39.
                    X-ray photon (λ = 0.01 Å) momentum is:
                    📅MOE 2008
                    Q40.
                    Energy of green light photon (λ = 5000 Å) is:
                    Q41.
                    Energy of photon (λ = 6600 Å) in eV is:
                    Q42.
                    Radio transmitter (1000 kHz, 66W) emits how many photons/second?
                    Q43.
                    Light (1.5× threshold frequency). If frequency is halved, photoelectrons:
                    Q44.
                    Threshold frequency = ν0. If incident frequency doubles, K.E. becomes:
                    Q45.
                    If light frequency doubles in photoelectric experiment, stopping potential:
                    Q46.
                    Threshold wavelength = 5000 Å. Photoemission occurs with:
                    Q47.
                    Threshold wavelength = 5200 Å. Photoemission occurs with:
                    Q48.
                    Photon energy = 6 eV, maximum K.E. = 4 eV. Stopping potential is:
                    Q49.
                    Green light ejects electrons; yellow does not. Red light will:
                    Q50.
                    Stopping potential is V when λ = λ. For λ = 2λ, stopping potential = V/3. Threshold λ is:
                    Q51.
                    Photoelectrons have K.E. ratio 1:K for frequencies ν1 and ν2 (ν1 > ν2). Threshold frequency is:
                    Q52.
                    Work function = 2.2 eV. Maximum wavelength for photoemission is:
                    📅MOE Bangladesh 2009
                    Q53.
                    Radiation with photon energies 2φ and 10φ incident on metal. Ratio of maximum photoelectron velocities:
                    Q54.
                    Photon energy = 5 eV, threshold frequency = 1.6 × 1015 Hz. K.E. of photoelectron (in eV):
                    📅KU 2014
                    Q55.
                    Cutoff potential = V0 at 1m. If source is moved to 2m, cutoff potential becomes:
                    Q56.
                    Speed of electron with λ = 10-10 m is:
                    Q57.
                    K1 and K2 are maximum K.E. for wavelengths λ1 and λ2. If λ1 = 3λ2, then:
                    📅BP 2014
                    Q58.
                    Work functions: A = 1.92 eV, B = 2.0 eV, C = 5 eV. Which emit photoelectrons for λ = 4100 Å?
                    Q59.
                    For a metal, ν = 2ν0 gives vmax = 4 × 106 m/s. If ν = 5ν0, vmax will be:
                    Q60.
                    X-rays on sodium and copper surfaces. Stopping potential is:
                    Q61.
                    Monochromatic source at distance 'd' emits n electrons/s with K.E. = E. At distance d/2:
                    Q62.
                    UV light (λ = 300 nm, I = 1.0 W/m²) on photosensitive material (1% efficiency). Photoelectrons emitted from 1.0 cm² area:
                    Q63.
                    Particle (mass 5m) decays into 2m and 3m. Ratio of de Broglie wavelengths:
                    Q64.
                    Proton and α-particle accelerated through same V. Ratio of de Broglie wavelengths:
                    Q65.
                    Proton (λ = λ) accelerated through V volt. To get same λ for α-particle, potential needed is:
                    Q66.
                    Particles with same velocity. Maximum de Broglie wavelength is for:
                    Q67.
                    Electron and photon with same λ have same:
                    Q68.
                    Energy added to electron to reduce λ from 10-10 m to 0.5 × 10-10 m:
                    Q69.
                    Electron and photon have same K.E. = 10-20 J. Their wavelengths relate as:
                    Q70.
                    Electron accelerated from 20V to 40V. de Broglie wavelength at 40V:
                    Q71.
                    de Broglie wavelength order for e-, p, n, α with same K.E.:
                    Q72.
                    Initial momentum of electron if momentum change Δp = pm causes 0.5% λ change:
                    Q73.
                    Ratio of momentum of e- and α accelerated through 100V:
                    Q74.
                    de Broglie wavelength of particle (rest mass m0) moving at c:
                    Q75.
                    Photon momentum = 3.3 × 10-27 kg m/s. Frequency is:
                    Q76.
                    Ratio of de Broglie wavelengths of proton and α with same energy:
                    📅IOM/BPKIHS
                    Q77.
                    de Broglie wavelength of electron in first Bohr orbit:
                    Q78.
                    Particle (v = 2.25 × 108 m/s) has same λ as photon. Ratio of K.E./Ephoton:
                    Q79.
                    If K.E. of free electron doubles, de Broglie wavelength changes by factor:
                    Q80.
                    Uncertainty in electron position = 10-10 m. Minimum uncertainty in momentum:
                    Q81.
                    Laser pulse period = 0.25 μs. Uncertainty in energy:
                    Q82.
                    Uncertainty in proton speed (Δx = 6 × 10-8 m):
                    Q83.
                    Electron velocity accuracy = 0.005%. Position measurement accuracy:
                    Q84.
                    Electron excitation time = 10-6 μs. Uncertainty in photon frequency:
                    Q85.
                    de Broglie wavelength of neutron at 927°C is λ. At 27°C, it is:
                    Q86.
                    Wavelength of 10 keV electron:
                    Q87.
                    Particles A (+q) and B (+4q) with same mass 'm' fall through same V. Ratio vA/vB:
                    Q88.
                    de Broglie wavelength of body (mass m, energy E):
                    📅IOM 2015
                    Q89.
                    Quantum theory is explained by:
                    📅KU 2016
                    Q90.
                    Radioactive particle decays into two pieces. Ratio of de Broglie wavelengths λ1/λ2:
                    📅IOM 2016