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Wize University Chemistry Textbook > Early Atomic Theory to Quantum Theory

The Photoelectric Effect

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The Photoelectric Effect

In 1905, Einstein conducted his photoelectric effect experiment.

  • The apparatus is made of a metal grid in which light of different intensities and frequencies was shown onto it.
  • The ammeter (A) measures current (the number of electrons emitted).
  • The voltmeter (V) measures the stopping potential (the energy of the electrons emitted).

Experimental Findings

1) 1 photon with sufficient energy to eject an electron:


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2) 1 photon with insufficient energy to eject an electron
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3) Multiple photons hitting the metal, individually they have insufficient energy to eject an electron but if you add up the their energy they have more energy than required to eject an electron



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4) Multiple photons, each with sufficient energy needed to eject an electron hitting the metal



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5) A photon with an increased frequency than the photons with minimum sufficient energy to eject an electron



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Summary of the Findings:

  • Electrons must be ejected by 1:1, photon : electron collisions
  • Increased intensity of the light (more photons for a given part of the light beam), increased the number of electrons emitted (if each of the photons had sufficient energy to eject electrons)
  • Increased frequency of the light, increased the energy of the electrons emitted


Before this experiment, people thought of light only as WAVES, but Einstein showed that light could also be thought of as particles (photons).
  • When particle A hits particle B, particle A transfers its momentum to particle B. This is not the case for waves!
  • The photoelectric effect showed that light can behave like particles since photons of light can hit a solid substance and cause electrons to be emitted

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Photoelectric Effect Equation

This experiment shows that light can behave like a particle “knocking” electrons out of a material.



  • The y-axis shows the kinetic energy (Ek) of the emitted electron
  • The x-axis shows the frequency of the photon that is hitting the metal's surface
  • When the frequency is too low, the energy of the photon is too low and an electron is not emitted
  • When the frequency reaches the threshold frequency, there is enough energy to emit an electron
  • At even higher frequencies, the kinetic energy (Ek) of the electron is increased further!

The energy corresponding to vo is called the ‘binding energy’ and represents the amount of energy required to remove the electron, EBinding

Ek electron being ejected =Ephoton −Ebinding\boxed{Ek\ _{electron\ being\ ejected}\ =E_{photon}\ -E_{binding}}

where Ephoton=hv=hcλwhere\ E_{photon}=hv=\frac{hc}{\lambda }
and Ekelectron=12mv2and\ Ek_{electron}=\frac{1}{2}mv^2
and Ebinding=minimum amount of energy needed to eject an electron


Wize Tip
The binding energy for each metal is unique.
Example: The binding energy of iron and gold are different.

The binding energy for a specific metal is constant so if you are given the binding energy for iron in a question, you can use that for part a) b) c) for example.

Does an electron get displaced when Ephoton > or < than Ebinding?
Ephoton> Ebinding means that the electron will have KE and it will get displaced!


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Example: Ejecting an Electron


When lithium metal is irradiated by a laser with a wavelength of 400 nm no electrons are ejected from the surface. If you want to ionize lithium which of the following types of radiation should you use?

a) UV-Laser
b) IR-Radiation
c) Red Light Laser
d) Green Light Laser
e) Radio Wave

If the 400 nm light (purple light) does not eject photons then the energy of the photon must be less than the work function (binding energy). Therefore we need a higher energy (shorter wavelength) photon.
Of the options listed only the UV-Laser will be higher energy than 400 nm laser. Answer is A

Wize Tip
When you see a question that mentions electrons being ejected from the surface of a metal, you know the question is going to have something to do with the photoelectric effect!

Practice: No Electrons are Ejected


A metal surface is irradiated by light from a laser with a wavelength of 492 nm. No electrons are measured leaving the surface. What is the most likely explanation?

Practice: Calculate the Binding Energy

An element is bombarded with a beam of X-rays of wavelength 0.75664nm. Upon irradiation, electrons are ejected with a velocity of 2.35x107 m/s. The mass of an electron is 9.11x10-31kg.

What is the binding energy for the element?
h=6.626x10-34 Js
Extra Practice
If a photon was able to remove an electron from a metal plate that had a binding energy of 2 x 10-20 J, what was the frequency of the wave?
If the answer has an exponent write it like this 1.23x10^4 (no spaces)
Work Function
The work function of metallic cesium is 3.36×10−19 J. What is the threshold wavelength of light required to emit electrons from the surface of metallic cesium?
Photoelectric Effect
The threshold wavelength for a neodymium (Nd) metal surface is 387 nm. What wavelength of light causes electrons to be ejected from the surface with a maximum kinetic energy of 1.473×10−18 J? (Choose the closest answer.)
Work Function
X-ray of frequency 1.53 ⋅\cdot 1016 Hz cause emission of electrons from a metal surface with a maximum kinetic energy of 1.313 ⋅\cdot 106 Jmol−1. Calculate the threshold frequency of the material.
Photoelectric effect: Threshold frequency
If we are told that a certain metal's threshold frequency to displace an electron is 9.12x1014Hz and we shine violet light (400nm) on the metal, would an electron be displaced?
Let's first write out our light equations so we can be reminded of how the variables are related:
E=hv c=λ(v)
An element is bombarded with a beam of X-rays of wavelength 0.75664 nm. Upon irradiation electrons are ejected with a velocity of 2.35 x 107 m/s.
Photoelectric effect: Work Function of Platinum
The binding energy for a material, sometimes know as the work function, can be found by irradiating a surface with a laser of sufficiently high energy and then measuring the kinetic energy of the ejected electrons. A researcher has found a new morphology of Platinum and is wondering if the work function has been modified. To test this the researcher irradiates the new form of Platinum with a UV-Laser with a wavelength of 125 nm and measures the kinetic energy of the electrons being ejected at 5.74 x 10-19 J. What is the work function of the new Platinum morphology? (1.60 x 10-19J = 1 eV)
Photoelectric effect: Binding Energy of Platinum
The binding energy for a material, sometimes known as the work function, can be found by irradiating a surface with a laser of sufficiently high energy and then measuring the kinetic energy of the ejected electrons. A researcher has found a new morphology of Platinum and is wondering if the binding energy has been modified. To test this the researcher irradiates the new form of Platinum with a UV-Laser with a wavelength of 125 nm and measures the kinetic energy of the electrons being ejected at 5.74 x 10-19 J. What is the binding energy of the new Platinum morphology? (1.60 x 10-19J = 1 eV)
The binding energy of Fe(s) is 612 kJ/mol.
a) What is the longest wavelength of light that can ionize a sample of iron metal? (Report your answer to three significant figures in nm; do not include the unit in the answer field)
b) Iron is irradiated with light of wavelength 12nm. What velocity does the electron leave the surface with? (Report your to three significant figures in scientific notation in m/s; do not include the unit in the answer field)
Periodic Trends: Ionization of an Excited Hydrogen Atom
A sample of hydrogen atoms is thermally excited so that the electrons are resting in the n=3 state. What is the wavelength of the lowest energy photon capable of ionizing these excited hydrogen atoms?
Elements: Binding Energy
An element is bombarded with a beam of X-rays of wavelength 0.75664nm. Upon irradiation, electrons are ejected with a velocity of 2.35 x 107 m/s.
What is the binding energy for the element?
Photoelectric effect: Practice
A metal surface is irradiated by light from a laser with a wavelength of 492 nm. No electrons are measured leaving the surface. What is the most likely explanation