Stopping potential depends on nature of photosensitive surface
•
Stopping potential becomes zero at threshold frequency
▢ Effect of Frequency and Wavelength:
Table 1: Frequency / Wavelength Change
Change
Effect on \(K_{max}\) / stopping potential
Frequency doubled
More than doubled
Frequency halved
Less than halved
Wavelength doubled
Less than halved
Wavelength halved
More than doubled
Below threshold frequency
No photoemission
Above threshold wavelength
No photoemission
▢ 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 1: de Broglie Wavelength Shortcuts
Particle
Wavelength
Electron
\(\lambda_e=\frac{12.34}{\sqrt V}\ Å\)
Alpha particle
\(\lambda_\alpha=\frac{0.101}{\sqrt V}\ Å\)
Proton
\(\lambda_p=\frac{0.286}{\sqrt V}\ Å\)
Deuteron
\(\lambda_d=\frac{0.202}{\sqrt V}\ Å\)
❖ 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 1: Particles
Particle
Mass
Charge
Proton
\(m_p\approx1.67\times10^{-27}kg\)
\(+e\)
Electron
\(m_e\approx9.1\times10^{-31}kg\)
\(-e\)
Deuteron
\(m_d\approx2m_p\)
\(+e\)
Triton
\(m_t\approx3m_p\)
\(+e\)
Alpha particle
\(m_\alpha\approx4m_p\)
\(+2e\)
Photon
\(m_0=0\)
0
▢ 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 1: Compton Effect Formulae
Quantity
Formula / Point
Compton shift
\(\Delta\lambda=\frac{h}{m_0c}(1-\cos\phi)\)
Scattering angle
\(\phi\)
Compton wavelength of electron
\(\lambda_C=\frac{h}{m_ec}\approx0.024Å\)
At \(\phi=0^\circ\)
\(\Delta\lambda=0\)
At \(\phi=180^\circ\)
\(\Delta\lambda_{max}=\frac{2h}{m_ec}\)
❖ 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 1: Answers
Q
Ans
1
b
2
d
3
b
4
a
5
a
6
d
7
b
8
c
9
a
10
d
11
b
12
d
13
c
14
b
15
b
16
a
17
c
18
c
19
a
20
a
21
d
22
d
23
d
24
b
25
a
26
b
27
a
28
c
29
d
30
a
31
d
32
b
33
b
34
a
35
b
36
a
37
b
38
c
39
d
40
b
41
a
42
c
43
b
44
c
45
d
46
c
47
c
48
d
49
c
50
b
51
d
52
b
53
b
54
b
55
d
56
d
57
d
58
a
59
b
60
c
61
b
62
b
63
c
64
c
65
d
66
b
67
d
68
d
69
b
70
b
71
a
72
b
73
c
74
c
75
d
76
b
77
a
78
a
79
d
80
b
81
b
82
b
83
c
84
b
85
b
86
b
87
a
88
a
89
b
90
c
91
a
92
c
▢ High-Yield Recall:
Table 1: Photoelectric Effect One-Liners
Fact
Answer
Photon energy
\(E=h\nu=\frac{hc}{\lambda}\)
Photon momentum
\(p=\frac{h}{\lambda}\)
Photon mass
\(m=\frac{h}{c\lambda}\)
Photon rest mass
0
Photoelectric effect
Emission of electrons by light
Best photoelectric metal
Cesium
Work function
\(\phi=h\nu_0=\frac{hc}{\lambda_0}\)
Einstein equation
\(h\nu=\phi+K_{max}\)
Maximum KE
\(K_{max}=h(\nu-\nu_0)\)
Stopping potential
\(eV_0=K_{max}\)
Photocurrent
\(\propto\) intensity
Stopping potential
\(\propto\) frequency
Number of electrons
\(\propto\) intensity
Maximum KE
Independent of intensity
Threshold frequency
Minimum frequency for photoemission
Threshold wavelength
Maximum wavelength for photoemission
Slope of \(V_0\)-\(\nu\) graph
\(h/e\)
de Broglie wavelength
\(\lambda=\frac{h}{p}\)
de Broglie wavelength by KE
\(\lambda=\frac{h}{\sqrt{2mK}}\)
Electron wavelength shortcut
\(\lambda=\frac{12.34}{\sqrt V}\ Å\)
Heisenberg principle
Uncertainty of conjugate quantities
Compton shift
\(\Delta\lambda=\frac{h}{m_ec}(1-\cos\phi)\)
Compton wavelength
\(0.024Å\)
Photoelectric effect proves
Particle nature of light
de Broglie hypothesis proves
Wave nature of matter
Q1.
To increase number of electrons emitted in photoelectric effect, increase
📅CEE MBBS 2025
Q2.
Quantum theory is explained by:
📅CEE Nursing 2024
Q3.
The work function of sodium is 2 eV. When light of wavelength 500 nm is incident on its surface, the maximum velocity of photoelectrons will be:
📅CEE MBBS 2024B
Q4.
If the work function of a metal is 4 eV and the velocity of the ejected electron is zero, then the wavelength of the incident photon is:
📅CEE MBBS 2024a
Q5.
Which of the following determines the saturation point for maximum photoelectric current?
📅CEE MBBS 2023
Q6.
In the photoelectric effect, the slope of the straight-line graph between stopping potential and frequency of incident radiation gives:
📅CEE MBBS 2023
Q7.
If the frequency of incident light is doubled, the stopping potential will be:
📅CEE MBBS 2021
Q8.
Find the number of photons emitted per second by a 600 MW monochromatic light source of wavelength 620 nm.
📅CEE MBBS 2021
Q9.
The threshold wavelength for the photoelectric effect from a metal surface is 5500 Å. The photoelectron will be emitted when illuminated with monochromatic radiation of:
📅CEE MBBS 2021
Q10.
Photon of energy 6 eV are incident on a metal surface whose work function is 4 eV. The minimum kinetic energy of the emitted photoelectron is:
📅CEE BDS 2024
Q11.
If \(V_2>V_1\) then, from the given photoelectric-current graph:
📅CEE BDS 2023
Q12.
If a photon has 100 eV energy then its frequency is
📅TOM 2009
Q13.
Planck's constant has the dimension of
📅MOE 2013
Q14.
If a pd of 1V is applied across an electron, the energy gained by it will be
📅MOE 2012
Q15.
Electron, proton, neutron and alpha particle have the same K.E. Which has the highest de-Broglie wavelength?
📅MOE 2012 & 2068
Q16.
A metal (work function 3.31 eV) is illuminated by light of wavelength 5×\(10^{-7}\) m. The threshold frequency is:
📅MOE 2010
Q17.
Light (λ=400nm) on metal (threshold λ=600nm) produces current I. If λ is doubled, photoelectric current will be:
📅MOE 2068
Q18.
If K.E. of a particle increases by four times, de-Broglie wavelength becomes:
📅MOE 2010
Q19.
The de-Broglie wavelength of electron is 1.224 Å. The energy of electron in eV is:
📅MOE 2010
Q20.
An electron (mass 'm', charge 'e') is accelerated from rest through pd. 'V' volts. Its speed will be:
Q21.
For light of fixed frequency above the threshold, the number of photoelectrons emitted per second primarily depends on:
📅KU 2012
Q22.
The wavelength associated with an electron (mass m, velocity v) is:
📅KU 2011
Q23.
A metal has work function \(2\,\mathrm{eV}\). What is the approximate maximum speed of a photoelectron emitted by \(230\,\mathrm{nm}\) light?
📅KU 2010
Q24.
Which wavelength falls under visible light?
Q25.
Which has frequency 6 × \(10^{15}\) Hz?
📅BP 2012
Q26.
Two photons move in opposite directions in a laboratory frame. What is their rate of separation in that frame?
📅I.E. 2009
Q27.
Photoelectric effect is explained by:
📅I.E. 2009
Q28.
An α-particle and proton accelerated through same potential. Ratio of final velocities:
📅I.E. 2011
Q29.
Particle nature of light is shown by:
📅TOM 2014
Q30.
Light (1.5× threshold frequency) on material. If frequency is halved and intensity doubled, photocurrent becomes:
📅MOE 2014
Q31.
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
Q32.
Which phenomenon does NOT support the wave theory of light?
📅BP 2014
Q33.
For a fixed incident light frequency above threshold, what happens to the maximum photoelectron kinetic energy as the metal’s threshold frequency increases?
📅BP 2014
Q34.
Value of Planck’s constant (h) is:
📅BP 2014
Q35.
The uncertainty in a proton’s position is \(6\times10^{-8}\,\mathrm m\). What is the minimum uncertainty in its speed?
📅BP 2014
Q36.
Ratio of de Broglie wavelengths of proton and α-particle with same K.E.:
📅BP 2014
Q37.
Work function = 3.3 eV. Threshold frequency is:
📅MOE 066
Q38.
UV photon (work function = 2 eV) produces photoelectron with 2 eV energy. Photon wavelength is:
📅MOE 2065
Q39.
Which conservation law is explicitly expressed by Einstein’s photoelectric equation \(hf=\phi+K_{\max}\)?
📅MOE 2063
Q40.
Light (frequency 3\(ν_{0}\)) on material. If frequency is halved and intensity doubled, photocurrent becomes:
Q41.
For fixed incident frequency above threshold, the number of photoelectrons emitted per second is proportional to:
📅I.E. 06
Q42.
Photoelectrons from a monochromatic beam have:
📅BPKIHS-08
Q43.
Increasing light intensity affects:
📅BPKIHS 02
Q44.
When frequency increases:
📅BPKIHS 02
Q45.
Photocell current is:
📅BPKIHS-04
Q46.
UV radiation (6.2 eV) on aluminum (φ = 4.2 eV). \(K.E._{max}\) is:
📅BPKIHS 05
Q47.
For photoemission to be energetically possible, the incident light frequency must be:
📅BPKIHS 05
Q48.
Photoelectric effect proves the existence of:
Q49.
Number of photons for fixed energy varies:
Q50.
X-ray photon (λ = 0.01 Å) momentum is:
📅MOE 2008
Q51.
Energy of green light photon (λ = 5000 Å) is:
Q52.
Energy of photon (λ = 6600 Å) in eV is:
Q53.
Radio transmitter (1000 kHz, 66W) emits how many photons/second?
Q54.
Light (1.5× threshold frequency). If frequency is halved, photoelectrons:
Q55.
A metal is illuminated with light of frequency \(1.5f_0\), where \(f_0\) is its threshold frequency. If the frequency is doubled, the maximum photoelectron kinetic energy becomes:
Q56.
In a photoelectric experiment, the incident frequency is initially above threshold. If it doubles while the metal remains unchanged, the stopping potential:
A metal has threshold wavelength \(520\,\mathrm{nm}\). Which of the following can produce photoemission?
Q59.
Photon energy = 6 eV, maximum K.E. = 4 eV. Stopping potential is:
Q60.
Green light ejects electrons; yellow does not. Red light will:
Q61.
Light of wavelength \(\lambda\) gives stopping potential \(V\), while light of wavelength \(2\lambda\) gives stopping potential \(V/3\) for the same metal. What is its threshold wavelength?
Q62.
The maximum photoelectron kinetic energies for incident frequencies \(f_1>f_2\) are in the ratio \(K_1:K_2=1:k\), with \(0
Q63.
Work function = 2.2 eV. Maximum wavelength for photoemission is:
📅MOE Bangladesh 2009
Q64.
Radiation with photon energies 2φ and 10φ incident on metal. Ratio of maximum photoelectron velocities:
Q65.
A photon of energy \(5\,\mathrm{eV}\) falls on a metal with threshold frequency \(1.6\times10^{15}\,\mathrm{Hz}\). What happens?
📅KU 2014
Q66.
Cutoff potential = \(V_{0}\) at 1m. If source is moved to 2m, cutoff potential becomes:
Q67.
Speed of electron with λ = \(10^{-10}\) m is:
Q68.
\(K_{1}\) and \(K_{2}\) are maximum K.E. for wavelengths \(λ_{1}\) and \(λ_{2}\). If \(λ_{1}\) = 3\(λ_{2}\), then:
📅BP 2014
Q69.
Work functions: A = 1.92 eV, B = 2.0 eV, C = 5 eV. Which emit photoelectrons for λ = 4100 Å?
Q70.
For a metal, ν = 2\(ν_{0}\) gives \(v_{max}\) = 4 × \(10^{6}\) m/s. If ν = 5\(ν_{0}\), \(v_{max}\) will be:
Q71.
X-rays on sodium and copper surfaces. Stopping potential is:
Q72.
Monochromatic source at distance 'd' emits n electrons/s with K.E. = E. At distance d/2:
Q73.
UV light (λ = 300 nm, I = 1.0 W/m²) on photosensitive material (1% efficiency). Photoelectrons emitted from 1.0 cm² area:
Q74.
A particle initially at rest decays into two fragments of masses 2m and 3m. What is the ratio of their de Broglie wavelengths?
Q75.
Proton and α-particle accelerated through same V. Ratio of de Broglie wavelengths:
Q76.
Proton (λ = λ) accelerated through V volt. To get same λ for α-particle, potential needed is:
Q77.
Particles with same velocity. Maximum de Broglie wavelength is for:
Q78.
Electron and photon with same λ have same:
Q79.
Energy added to electron to reduce λ from \(10^{-10}\) m to 0.5 × \(10^{-10}\) m:
Q80.
Electron and photon have same K.E. = \(10^{-20}\) J. Their wavelengths relate as:
Q81.
An electron is accelerated from rest through \(40\,\mathrm V\). What is its approximate de Broglie wavelength?
Q82.
de Broglie wavelength order for \(e^{-}\), p, n, α with same K.E.:
Q83.
The magnitude of an electron’s momentum changes by \(\Delta p=p_m\), producing approximately a 0.5% change in its de Broglie wavelength. What was its initial momentum (small-change approximation)?
Q84.
Ratio of momentum of \(e^{-}\) and α accelerated through 100V:
Q85.
For a particle with nonzero rest mass, what happens to its de Broglie wavelength as its speed approaches the speed of light?
Q86.
Photon momentum = 3.3 × \(10^{-27}\) kg m/s. Frequency is:
Q87.
Ratio of de Broglie wavelengths of proton and α with same energy:
📅IOM/BPKIHS
Q88.
de Broglie wavelength of electron in first Bohr orbit:
Q89.
Using the nonrelativistic kinetic-energy formula, a particle of speed \(v=2.25\times10^8\,\mathrm{m/s}\) has the same de Broglie wavelength as a photon. What is the formal classical value of \(K/E_{\mathrm{photon}}\)?
Q90.
If K.E. of free electron doubles, de Broglie wavelength changes by factor:
Q91.
Uncertainty in electron position = \(10^{-10}\) m. Minimum uncertainty in momentum:
Q92.
If the lifetime of an excited state is approximately \(0.25\,\mu\mathrm{s}\), what is the order of its minimum energy uncertainty?
Q93.
Uncertainty in proton speed (Δx = 6 × \(10^{-8}\) m):
Q94.
An electron moves at \(2.5\times10^3\,\mathrm{m/s}\) and its speed is measured with a relative uncertainty of \(0.005\%\). What is the minimum position uncertainty?
Q95.
An excited atomic state has lifetime \(10^{-6}\,\mu\mathrm s\). Using \(\Delta E\Delta t\ge\hbar/2\) and \(E=hf\), estimate the minimum frequency uncertainty.
Q96.
de Broglie wavelength of neutron at 927°C is λ. At 27°C, it is:
Q97.
Wavelength of 10 keV electron:
Q98.
Particles A (+q) and B (+4q) with same mass 'm' fall through same V. Ratio \(v_{A}\)/\(v_{B}\):
Q99.
de Broglie wavelength of body (mass m, energy E):
📅IOM 2015
Q100.
Quantum theory is explained by:
📅KU 2016
Q101.
A particle initially at rest decays into exactly two fragments. What is the ratio of their de Broglie wavelengths?
