Physics Lesson 19.2.2 - Einstein's Equation of Photoelectric Effect. The Particle Nature of Light

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Welcome to our Physics lesson on Einstein's Equation of Photoelectric Effect. The Particle Nature of Light, this is the second lesson of our suite of physics lessons covering the topic of The Photoelectric Effect, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Einstein's Equation of Photoelectric Effect. The Particle Nature of Light

The phenomenon of photoelectric effect was explained by Einstein in 1905, who accepted as true the Planck's hypothesis on the discrete nature of light. Einstein elaborated further this idea by asserting that light is emitted, propagated and absorbed in specific portions (quanta) of energy. He supported the idea of the discrete nature of light and that light is composed by microscopic particles (photons) having the energy E_photon = h · f and impulse p = E / c.

Here, c represents the speed of light particles or photons. Einstein considered the proton-electron interaction to explain the photoelectric effect and he applied the law of conservation of energy for this. Thus, the electron near the metal surface "absorbs" the photon and "consumes" part of photons energy (E = h · f) during its detachment from metal. This energy is known as Work Function, Φ and represent the minimum work necessary to detach the electron from metal. When the energy of incident photon absorbed by the electron during the photoelectric effect is greater than the work function, the electron gains kinetic energy and thus, it can escape from metal. In this way, the Einstein's Equation of Photoelectric Effect derived from the law of conservation of energy, is

Energy of Photon = Work Function + Kinetic Energy of Electron

h ∙ f = Φ + KE

Remark! Do not confuse the light flux Φ with the work function Φ in the photoelectric effect. They are completely different things. The first (light flux) is measured in Lumen, lm, which is candela times steradian (1 lm = 1 cd · sr), while work function Φ has the unit of energy (Joule).

The table below shows the work function in electronvolts, e_V (1e_V = 1.6 × 10^-19 J) for a number of metals.

Physics Tutorials: This image provides visual information for the physics tutorial The Photoelectric Effect

It is an interesting fact that Einstein won the Nobel Prize for explaining the phenomenon of photoelectric effect but did not win any Nobel Prize for his discoveries in relativity. This is because nobody from the Nobel Prize committee was able to understand in-depth his idea on relativity at that time.

Example 1

Calculate the wavelength of photon needed to make an electron move at 6 × 10⁶ m/s towards the anode during the photoelectric effect. The cathode is made of tungsten. Take me ≈ 9.1 × 10^-31 kg.

Solution 1

From the table above we see that the work function of tungsten is

Φ = 4.50 eV
= 4.50 ∙ 1.6 × 10^-19 J
= 7.2 × 10^-19 J

First, we must find the frequency of the incident photon, f_ph. From the Einstein's Equation of Photoelectric Effect, we have

h ∙ f_ph = Φ + m_e ∙ v_e²/2
f_ph = Φ + m_e ∙ v_e²/2/h
= (7.2 × 10^-19 J) + (9.1 × 10^-31 kg) ∙ (6 × 10⁶ m/s)²/2/6.626 × 10^-34 J ∙ s
= 2.58 × 10¹⁶ Hz

Giving that for all EM waves we have

c = λ ∙ f

where c = 3 × 10⁸ m/s, we obtain for the wavelength λ_ph of the incident photon:

λ_ph = c/f_ph
= 3 × 10⁸ m/s/2.58 × 10¹⁶ Hz
= 1.163 × 10^-8 m
= 11.63 nm (UV radiation)

When the electron-photon interaction occurs at the surface of metal, the kinetic energy resulting from the photoelectric effect has a higher value than when this interaction occurs inside the metal. This is because electron transmits some of its kinetic energy to the metal atoms during collisions taking place when it in on the way to move to the metal surface. The kinetic energy of electron in Einstein's Equation of Photoelectric Effect represents the maximum kinetic energy of electron, i.e. when applying this equation we assume the electron is on the surface of metal, not inside it.

You have reached the end of Physics lesson 19.2.2 Einstein's Equation of Photoelectric Effect. The Particle Nature of Light. There are 3 lessons in this physics tutorial covering The Photoelectric Effect, you can access all the lessons from this tutorial below.

More The Photoelectric Effect Lessons and Learning Resources

Modern Physics Learning Material
Tutorial ID	Physics Tutorial Title	Revision Notes	Revision Questions
19.2	The Photoelectric Effect
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
19.2.1	Laws of the Photoelectric Effect
19.2.2	Einstein's Equation of Photoelectric Effect. The Particle Nature of Light
19.2.3	Explanation of the Laws of Photoelectric Effect

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