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Questions and Answers
What is the name of the hypothesis that associates a fictitious wave with any body or particle with momentum 'p'?
What is the name of the hypothesis that associates a fictitious wave with any body or particle with momentum 'p'?
De-Broglie Hypothesis
What is the relation between the momentum 'p' and the wavelength 'λ' of a wave associated with a particle?
What is the relation between the momentum 'p' and the wavelength 'λ' of a wave associated with a particle?
h / p
What is the term used to describe a device that converts a signal in one form of energy to another?
What is the term used to describe a device that converts a signal in one form of energy to another?
Transducer
What type of device is a pressure sensor?
What type of device is a pressure sensor?
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What type of sensor is used to monitor the pressure of gases or fluids in a pipeline?
What type of sensor is used to monitor the pressure of gases or fluids in a pipeline?
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What are the two energy bands involved in Energy-bands in a Solid?
What are the two energy bands involved in Energy-bands in a Solid?
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In an insulator, the energy gap (Eg) is much larger than the thermal energy (kT).
In an insulator, the energy gap (Eg) is much larger than the thermal energy (kT).
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What is the relationship between the total magnetic flux through an arbitrary closed surface 'A' and the divergence of magnetic fields?
What is the relationship between the total magnetic flux through an arbitrary closed surface 'A' and the divergence of magnetic fields?
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What is the name of the law that establishes the relationship between Magnetic and Electric fields, describing how a changing magnetic flux results in circulation of Electric-field?
What is the name of the law that establishes the relationship between Magnetic and Electric fields, describing how a changing magnetic flux results in circulation of Electric-field?
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What is the name of the law that describes how changing Electric flux through arbitrary surface 'A' results in circulation of Magnetic-field?
What is the name of the law that describes how changing Electric flux through arbitrary surface 'A' results in circulation of Magnetic-field?
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A wave function must be discontinuous to be physically valid.
A wave function must be discontinuous to be physically valid.
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A physically valid wave function must be quadratically integrable, requiring the integral Ψ*Ψ dτ to exist.
A physically valid wave function must be quadratically integrable, requiring the integral Ψ*Ψ dτ to exist.
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A physically valid wave function must be single-valued.
A physically valid wave function must be single-valued.
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A wave function must be orthogonal for a physically valid function.
A wave function must be orthogonal for a physically valid function.
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According to Heisenberg's Uncertainty Principle, the more precisely one property is measured (e.g., position), the less accurately the other property (e.g., momentum) can be known.
According to Heisenberg's Uncertainty Principle, the more precisely one property is measured (e.g., position), the less accurately the other property (e.g., momentum) can be known.
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In the equation for the Total Energy of a Simple Harmonic Motion (SHM), what is the relationship between the kinetic energy (Ek) and the potential energy (U) with time?
In the equation for the Total Energy of a Simple Harmonic Motion (SHM), what is the relationship between the kinetic energy (Ek) and the potential energy (U) with time?
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What is doping in Semi-Conductors?
What is doping in Semi-Conductors?
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What are the two types of extrinsic semiconductors?
What are the two types of extrinsic semiconductors?
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What is the phenomenon in which waves arriving at an interface from one medium to another are completely reflected back into the internal medium?
What is the phenomenon in which waves arriving at an interface from one medium to another are completely reflected back into the internal medium?
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What is a p-n junction connected to two electrical terminals called?
What is a p-n junction connected to two electrical terminals called?
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What is the name of the mathematical equation that describes the behavior of a wave function over time?
What is the name of the mathematical equation that describes the behavior of a wave function over time?
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What is the name of the mathematical equation that describes the behavior of a wave function at a given point in time?
What is the name of the mathematical equation that describes the behavior of a wave function at a given point in time?
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What does the normalization condition for a wave function state about the probability of finding a particle within the entire space?
What does the normalization condition for a wave function state about the probability of finding a particle within the entire space?
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What is the minimum distance between particles vibrating in phase with each other in a wave?
What is the minimum distance between particles vibrating in phase with each other in a wave?
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What is the maximum displacement of a particle in the wave from its rest or equilibrium position?
What is the maximum displacement of a particle in the wave from its rest or equilibrium position?
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What is the number of oscillations (cycles) per unit time called?
What is the number of oscillations (cycles) per unit time called?
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What is the amount of time per cycle called?
What is the amount of time per cycle called?
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What happens when the path difference between two waves is an integral multiple of the wavelength (λ)?
What happens when the path difference between two waves is an integral multiple of the wavelength (λ)?
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What happens when the path difference between two waves is an odd multiple of half the wavelength?
What happens when the path difference between two waves is an odd multiple of half the wavelength?
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What is the theoretical speed of electromagnetic waves (EMWs)?
What is the theoretical speed of electromagnetic waves (EMWs)?
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What type of rays are used to kill germs in water purifiers?
What type of rays are used to kill germs in water purifiers?
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What type of rays are used in Radiotherapy to kill cancerous cells?
What type of rays are used in Radiotherapy to kill cancerous cells?
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What is a key principle behind the development of the wave-particle duality of Radiation/Light?
What is a key principle behind the development of the wave-particle duality of Radiation/Light?
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What is the theory that supports the particle nature of light?
What is the theory that supports the particle nature of light?
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What is the name of the law that describes the distribution of energy in black-body radiation?
What is the name of the law that describes the distribution of energy in black-body radiation?
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Match the following key-points with their corresponding wave or particle nature:
Match the following key-points with their corresponding wave or particle nature:
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Study Notes
Simple Harmonic Motion
- A periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position.
De-Broglie Hypothesis
- Any body or material particle with momentum 'p' is intrinsically associated with a fictitious wave (matter-wave) of wavelength 'λ'.
- This relationship is expressed as λ = h/p, where 'h' is Planck's constant.
Gauss's Law for Magneto-statics
- The total magnetic flux through an arbitrary closed surface 'A' is always zero (LHS=RHS).
- This means magnetic fields have no divergence.
- This rules out the existence of independent magnetic charges or poles.
Transducers and Sensors
- A transducer converts a signal from one form of energy to another.
- A sensor is a transducer that receives and responds to a signal or stimulus from a physical system.
- Pressure sensors monitor gas or fluid pressure in pipelines; a sudden drop might indicate a leak, triggering predefined actions (e.g., closing valves).
Energy-bands in a Solid
- Solid materials have valence bands and conduction bands.
- Insulators have large energy gaps (Eg » kT).
De-Broglie wavelength of an electron
- The de Broglie wavelength of an electron accelerated from rest through a potential difference of 650V is calculated using the Work-Energy theorem.
- The final result is λ = 4.81 x 10⁻¹¹ m.
Conditions for a Physically Valid Wave-function
- The wave function (Ψ(x, t)) must be continuous, and all its partial derivatives must also be continuous.
- The wave function (Ψ(x, t)) must be quadratically integrable.
- The integral (Ψ*Ψ dτ) must be single-valued.
- The wave function (Ψ(x, t)) must be normalized.
- The wave function (Ψ(x, t)) must be orthogonal
- The wave-function must be finite everywhere
- The wave function must satisfy the boundary conditions of the quantum mechanical system it represents.
Heisenberg's Uncertainty Principle
- There's a limit to the precision with which certain pairs of physical properties (e.g., position (x) and momentum (p)) can be known simultaneously.
- The more accurately one property is measured, the less accurately the other can be determined. This is represented by the equation σxσp ≥ h/4π.
Energies of SHM
- The total energy (Et) of a simple harmonic oscillator is constant and equal to the sum of kinetic and potential energies.
- Ek and U are dependent on time and equal 1/2 kA²cos²(wt + φ) and 1/2 kA²sin²(wt + φ), respectively.
Doping of Semi-Conductors
- Doping intentionally introduces impurities (trivalent or pentavalent) into intrinsic semiconductors to modify electrical, optical, and structural properties.
- This leads to p-type (trivalent doping) and n-type (pentavalent doping) extrinsic semiconductors.
Optical Fibres and TIR
- TIR is when waves arriving at an interface between mediums are completely reflected back into the medium (internal medium).
- The external medium has a lower refractive index, incident waves strike at a sufficient oblique angle to fully reflect.
- A Diode is a p-n junction electrically connected.
- TDSE and TISE are equations governing time-dependent and time-independent Schrödinger equations.
Probability of observing a particle
- Probability of finding a particle between given points (x₁ and X₂) is calculated through Ψ*(x)Ψ(x)dx
Plane Progressive Wave
- Wavelength (λ) is the distance between two successive points in a wave that are in phase.
- Amplitude is the maximum displacement of a particle experiencing the wave from its equilibrium position.
Frequency and Time-Period
- Frequency (v) is the number of oscillations per unit time (e.g. s⁻¹ or Hz).
- Time-period (T) is the time taken for one complete cycle.
Theoretical speed of EMWs and the EM-Spectrum
- The speed of electromagnetic waves (EMWs) is calculated by the relationship v2 =(1/(μ₀ε₀)).
- The universal value of this speed is approximately 2.998 x 10⁸ m/s.
Types of EM Radiation
- Radio Waves, used in communication
- Microwaves, used in navigation and heating
- Infrared, used in remote controls and thermal imaging
- Ultraviolet, used in water purification and anti-counterfeiting
- X-rays, used for imaging and crystallography
- Gamma Rays, used in radiotherapy and medical sterilization
- Visible light used for illumination and observation.
Historical Key-points on Wave-Particle Duality
- Wave and particle nature of light and radiation has historical key-points such as Huygens' Principle, Young's double-slit experiments, Arago's Spot, Maxwell and Hertz's work on EM waves, and Planck's Law for Black-Body Radiation, photoelectric effects, Compton Effects.
Energy Band Diagram
- Energy band diagrams illustrate how electrons fill or remain unoccupied in energy levels in a material.
- Conductor, Semiconductor, and Insulators are defined by different energy gaps (Eg).
Characteristics of a Semiconductor
- Semiconductor conductivity increases with temperature. This differs from other materials (e.g. insulators, or conductors)
Unit Vector
- A unit vector is a vector with a magnitude of 1. Often used to represent directions.
Dot Product of two vectors
- The dot product of two vectors is an algebraic operation that returns a single number (scalar).
- It's useful to detect vector orthogonality (angle of π/2). Geometrically, it's the scalar projection of one vector onto the direction of the other, scaled by the other vector's magnitude.
Magnitude of a Vector
- A vector's magnitude is its length.
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Description
Test your knowledge on fundamental physics concepts including Simple Harmonic Motion, the De-Broglie Hypothesis, Gauss's Law for Magneto-statics, and the functions of transducers and sensors. Each topic explores critical principles that are essential for understanding the complexities of physics in real-world applications.
