Abstract
In a basic physics course, one is introduced to the concept of particles and waves. The understanding evolves with the intuitive concepts of particles colliding with each other to exchange energy and momentum; and waves interacting with each other to create interference patterns. Such everyday observations may be explained by using Classical mechanics, also known as Newtonian mechanics. However, at the atomic scale, this simple everyday intuitive picture does not hold. Whether an electron behaves as a particle or a wave depends on the circumstances. Sometimes, it may collide with other electrons and barriers just like a particle. At times, it behaves like waves and in fact, creates interference patterns! It may also transmit through barriers, a phenomenon called quantum mechanical tunneling, which has no classical analog.
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- 1.
While speed is a scalar quantity, velocity is a vector. Scalar quantities are represented by magnitude only, whereas vectors have both magnitude and direction. In this text, we would not worry about the vector representation of these quantities, and would work with the magnitude only.
- 2.
Acceleration is a vector quantity. Even a change in the direction with constant speed gives rise to acceleration.
- 3.
Circular motion is a special type of curvilinear motion.
- 4.
Both degrees and radians are dimensionless units.
- 5.
Photons are Bosons. Therefore, multiple bosons may occupy the same energy state. In contrast, electrons are Fermions, and one energy state may house only one electron.
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Appendices
Problems
2.1 For \(E=1\) eV, calculate the frequency for a quantum particle. You may assume speed equal to that of the speed of light (c).
2.2 For \(E=1\) eV, calculate the wavelength for a quantum particle. You may assume speed equal to that of the speed of light (c).
2.3 For \(E=1\) eV, calculate the wavenumber for a quantum particle. You may assume speed equal to that of the speed of light (c).
2.4 For \(E=1\) eV, calculate the momentum. You may assume speed equal to that of the speed of light (c).
2.5 For a visible photon of wavelength \(0.5\,\upmu \mathrm{m}\), calculate the frequency and energy. What would be the color of light?
2.6 Calculate n (the number of Bosons) at \(T=300\) K for the data in Problem 2.5.
2.7 For an electron traveling at \(v=1\) m/s, calculate its wavelength.
2.8 For an electron traveling at \(v=10^3\) m/s, calculate its wavelength.
2.9 For an electron traveling at \(v=10^6\) m/s, calculate its wavelength.
2.10 For an electron traveling at \(v=0.9\) c, calculate its wavelength. c is the speed of light.
Research Assignment
R2.1 Various industrial and consumer applications of nanotechnology include plastics, textile fabrics, cosmetics, sports equipment, surfaces and coatings, etc. Pick a topic of your choice about how nanotechnology is impacting industrial and consumer applications, and write a one-page summary.
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Raza, H. (2019). Particle, Waves, and Duality. In: Freshman Lectures on Nanotechnology. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-11733-7_2
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DOI: https://doi.org/10.1007/978-3-030-11733-7_2
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-030-11733-7
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