The Photoelectric Effect in Cameras
- Page ID
- 418916
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. D. 1. a. Electromagnetic radiation can be characterized by wavelength or frequency, and different wavelengths of radiation are useful for different measurements of matter. a. The interaction of photons with molecules and atoms provides information about energy levels.
Cameras help to document the world around us and preserve moments in time. For most photographers, taking a photo requires a simple click of a button, making it easy to take the complexities involved in capturing an image for granted. We will explore the system within every camera that is hard at work absorbing electromagnetic radiation and shuttling electrons to different locations to produce the images that we see.
How do cameras capture images?
Most digital cameras today use image sensors called charge-coupled devices (CCD). A CCD is a type of sensor composed of layers of silicon which have been exposed to various elements like phosphorus and boron to alter its conductive properties (1). CCDs are covered in light sensitive “squares'' called pixels that are organized in a grid formation. Each pixel acts as a storage center for the electrons that are produced in the photoelectric effect. When a photon of light strikes the image sensor, the silicon material in the CCD absorbs the photons, and electrons are then released from the silicon material via the photoelectric effect. These released electrons move up to the surface of the silicon layer and are stored in the pixel grid. The electrons are then translated into a voltage level. An analog-to-digital converter then creates a digital number based on the voltage (2). These digital numbers are then used to create the image that we see produced from the camera (1).
Figure \(\PageIndex{1}\). CCD sensor from a digital camera (3)
What is the photoelectric effect?
The photoelectric effect was originally discovered by physicist Heinrich Rudolf Hertz in 1887. He observed that when ultraviolet light shines onto two metal electrodes with voltage running through them, light is emitted at different voltages. Following this discovery, Physicist Philipp Lenard showed that electrons are released from the metal surface when it is hit with light (4).
Material will absorb the photon’s electromagnetic radiation when hit with light. If the photons have sufficient energy, electrically charged electrons will be released from the material’s surface. This phenomenon is known as the photoelectric effect (4).
Figure \(\PageIndex{2}\). Photoelectric effect: blue line depicts applied energy used that performs work on the metal to remove one electron. The black arrow represents the kinetic energy with which the electron leaves the metal (5).
The number of emitted electrons and their relative kinetic energies depend on the intensity and frequency of the light. Intensity is the number of photons that are transmitted per unit area per unit time, while the amount of energy per photon relies on the wavelength (λ), frequency (ν), and speed (c) of a wave (c is the speed of light in a vacuum 3.0 x 10^8 m/s) (6).
Figure \(\PageIndex{3}\). Relationship between frequency and wavelength. Wavelength and frequency are inversely proportional – a high frequency corresponds to a short wavelength (7).
Wavelength is the distance between two identical points of the same phase on the wave. Frequency describes the number of waves that pass through a fixed point in a given amount of time (7). Wavelength and frequency are related by the formula:
\[λv =c\]
The relationship between intensity and frequency on the number of emitted electrons and their relative kinetic energies can be explained with the following equations:
\[E_{photon} =KE_{electron} +W_{electron}\]
\[hν = \frac{1}{2} mv^2 + Φ\]
A higher intensity means that there will be a greater number of emitted photoelectrons, and a higher frequency means that the emitted photoelectrons will have greater kinetic energy.
This relationship can also be represented in a graph:
Figure \(\PageIndex{4}\). The x-intercept of the graph is the threshold frequency of the material, which is the minimum frequency of light that a photo must be in order to have enough kinetic energy to eject an electron. The y-intercept of the graph is the work function of the material. The work function describes the minimum amount of energy needed to eject an electron from the material.
207.8 KJ of energy is needed to remove one mole of electrons from silicone in a camera CCD sensor. If the silicone in the camera CCD sensor is irradiated with 304 nm of light. What is the maximum kinetic energy the released electrons can have?
Solution
Given the minimum energy required to remove an electron from the silicone surface, 207.8 kJ, and the wavelength of the irradiated light, we can use Planck’s equation and the work function formula to find the maximum kinetic energy that the released electrons can have.
First, we must find the amount of applied energy in Joules using the equation:
\[E =hf = \frac{hc}{λ}\]
\[h = 6.626•10^{-34} \frac{m^2kg}{s}\]
\[c = 3.0•10^8 \frac{m}{s}\]
\[Φ= 304 nm = 3.04∙10^{-7} m\]
When we plug in the values above into Planck’s equation, we get:
\[E = \frac{(6.626∙10^{-34} \frac{m^2kg}{s})(3.0∙10^8\frac{m}{s})}{3.04∙10^{-7} m} = 6.54∙10^{-19} J\]
Because the work function is given in kilojoules, we must first convert it into joules:
\[Φ = \frac{207.8 kJ}{1 mole}•\frac{1 mole}{6.022∙10^{23} e^-}•\frac{1000 J}{1 kJ} = 3.54•10^{-19} J\]
Now we can solve for the maximum kinetic energy using the work-function equation:
\[KE=EA-Φ\]
\[KE=(6.54•10^{-19}J)-(3.54•10^{-19}J)=3.09•10^{-19}J\]
Therefore, the maximum kinetic energy that the released electrons can have based on the work function and applied energy is 3.09•10-19 J.
A camera detects an electrical signal of 2.18•10-19 J of energy from 8 electrons. If we assume only one wavelength of light hits the camera sensor and the work needed to remove one electron from the silicon in the camera is 4.60•10-19 J, what is the wavelength in nm? What color is the wavelength?
Use the table below:
| Color | Wavelength (nm) |
| Red | 630-750 |
| Orange | 590-630 |
| Yellow | 570-590 |
| Green | 490-570 |
| Blue | 450-490 |
| Indigo | 420-450 |
| Violet | 380-420 |
Solution
To solve for the kinetic energy of one electron, divide the total energy by the number of electrons
\[\frac{2.18•10^{-19}J}{8 e^-}= 2.725•10^{-20} \frac{J}{e^-}\]
To solve for the total energy of the incoming light that is applied to remove one election, use the equation. The given work function to remove one electron from the silicon is 300.2 kJ.
\[KE=EA-Φ\]
\[2.725•10^{-20} J+4.60•10^{-19} =EA\]
4.87•10^{-19}=EA\]
Since we know the activation energy, we can now solve for the wavelength
\[E =hf = \frac{hc}{λ}\]
\[4.87•10^{-19}=\frac{(6.626•10^{-34} \frac{m^2kg}{s})(3.0•10^8 \frac{m}{s})}{λ}\]
\[λ=4.08•10^{-7}m\]
Therefore, the wavelength of the light is 4.08•10-7m or 408nm. This wavelength corresponds to the color violet which has a wavelength range of 380 to 420 nanometers. This means that the wavelength of light that hits the camera sensor is violet.
Conclusion
The photoelectric effect is unfolding in every digital camera each time we take a picture. That embarrassing selfie your friend posted on Instagram - the photoelectric effect played a role in capturing that image! After you click your camera to capture an image, the absorbed photons eject electrons from the silicon material inside the camera and are then transported into rows where they are converted into the image we see on the screen. The next time you blame your friend for the embarrassing photo they posted of you on social media, try channeling your frustration towards the photoelectric effect instead.
References
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Corning, A. CCD Sensors, Albert Einstein, and the Photoelectric Effect. Radiant Vision Systems. https://www.radiantvisionsystems.com...hines%20on%20a (accessed 2022-12-05).
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Labelle, R.; Garvey, S. Introduction to High Performance CCD Cameras; IEEE, 1995. https://ieeexplore.ieee.org/document/519136 (accessed 2022-12-05).
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Wikipedia Contributors. Charge-coupled device. Wikipedia. https://en.wikipedia.org/wiki/Charge-coupled_device (accessed 2022-12-05).
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The Editors of Encyclopedia Britannica. Photoelectric Effect | Physics. Encyclopædia Britannica; 2018.
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Wikipedia Contributors. Photoelectric effect. Wikipedia. https://en.wikipedia.org/wiki/Photoelectric_effect (accessed 2022-12-05).
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Cooper, M. M.; Klymkowsky, M. W. 2.2 Taking Quanta Seriously. Chemistry LibreTexts. https://chem.libretexts.org/Bookshel...anta_Seriously (accessed 2023-05-14).
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The Editors of Encyclopaedia Britannica . Frequency | Definition, Symbols, & Formulas. Encyclopædia Britannica; 1998.
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Filmmaker IQ. The Science of Camera Sensors. Youtube. https://www.youtube.com/watch?v=MytCfECfqWc (accessed 2022-12-05).
If you want to learn more about this topic, check out these sites:
https://www.khanacademy.org/science/physics/quantum-physics/photons/a/photoelectric-effect (Provides a basic outline of the photoelectric effect)
https://ieeexplore.ieee.org/abstract/document/519136 (A research article that takes a deeper dive into CCD cameras and their performance)