p.7
Heisenberg Uncertainty Principle
What does the wave nature of matter introduce in terms of particle location?
An uncertainty in the location of the particle.
p.7
Davisson-Germer Experiment and Evidence of Matter Waves
Who provided the first experimental evidence of matter waves?
Davisson and Germer in 1927.
p.4
Planck's Hypothesis and Radiation Law
What is the famous formula for Black body radiation?
E = (8πhc/λ^5)(e^(hν/kT) - 1)
p.14
Schrodinger's Wave Equation and Particle in a Box
What is the normalized wave function ψ(x) after substituting A?
ψ(x) = √(2/L) sin(2nπx/L).
p.11
Schrodinger's Wave Equation and Particle in a Box
What does the wave function ψ represent?
It is a complex quantity representing the variation of matter wave.
p.14
Schrodinger's Wave Equation and Particle in a Box
What is the equation used to calculate the unknown constant A?
A² ∫ sin²(2nπx/L) dx = 1.
p.16
Band Theory of Solids and Electron Theory
What are valence electrons?
Electrons in the outermost shell that are free to move.
p.1
Wave-Particle Duality and Quantum Theory
What theory did Huygens propose in 1979 to explain light phenomena?
The wave theory of light.
p.2
Stefan-Boltzmann Law and Wien's Law
What is the relationship between the total emissive power (R) and absolute temperature (T) according to Stefan's Law?
R(T) = σT^4, where σ is Stefan’s Constant (5.67 x 10^-8 wm^-2 k^-4).
p.8
De Broglie's Concept of Matter Waves
What occurs to the bumps at higher potentials?
The bumps gradually disappear.
p.8
De Broglie's Concept of Matter Waves
What does the most prominent bump verify?
The existence of electron waves.
p.11
Schrodinger's Wave Equation and Particle in a Box
What is the physical significance of |ψ|²?
It is the probability density function.
p.19
Band Theory of Solids and Electron Theory
What does the Kronig-Penney model suggest about the potential energy of electrons in a crystal?
It varies due to the presence of immobile lattice ions.
p.9
Heisenberg Uncertainty Principle
What principle states that measuring the position accurately affects the measurement of momentum?
The Heisenberg Uncertainty Principle.
p.16
Band Theory of Solids and Electron Theory
What are core electrons?
Electrons in the closed shell that are strongly attracted by the nucleus.
p.7
Davisson-Germer Experiment and Evidence of Matter Waves
What is the purpose of the electron gun in Davisson-Germer's experiment?
To produce electrons through thermionic emissions.
p.7
Davisson-Germer Experiment and Evidence of Matter Waves
What happens to the electrons after they are emitted from the electron gun?
They are accelerated in an electric field of known potential difference.
p.8
De Broglie's Concept of Matter Waves
What does a nickel crystal act as in X-ray analysis?
A plane diffraction grating.
p.10
Wave-Particle Duality and Quantum Theory
What does the classical wave equation in differential form describe?
The behavior of a particle with wave properties.
p.2
Stefan-Boltzmann Law and Wien's Law
What does Wien's Law state about the wavelength corresponding to maximum energy (λm)?
λm is inversely proportional to absolute temperature (T), i.e., λmT = constant.
p.13
Schrodinger's Wave Equation and Particle in a Box
What is the boundary condition applied to the wave function in a box?
At the boundary, ψ = A sin(Kx) must equal zero.
p.16
Band Theory of Solids and Electron Theory
What is drift velocity?
The average velocity acquired by free electrons in a particular direction after an electric field is applied.
p.9
Heisenberg Uncertainty Principle
What does ΔE represent in the Heisenberg Uncertainty Principle?
The error in the measurements of energy.
p.5
De Broglie's Concept of Matter Waves
How is kinetic energy related to temperature?
E = 3/2 kT (where K is the Boltzmann constant)
p.10
Schrodinger's Wave Equation and Particle in a Box
What does ψ₀ represent in the wave function?
The amplitude at the point considered.
p.18
Band Theory of Solids and Electron Theory
What does the electrical conductivity of a metal measure?
The amount of electrical charge conducted per unit time across unit area per unit applied electrical field.
p.11
Schrodinger's Wave Equation and Particle in a Box
What does the integral ∫ψψ* dx dy dz equal if the particle is present?
1, known as the normalized condition of wave function.
p.19
Band Theory of Solids and Electron Theory
In the Kronig-Penney model, where is the potential of an electron at the positive ion site?
Zero, and it is maximum between two ions.
p.9
Heisenberg Uncertainty Principle
What does Δx represent in the context of the microscope?
The uncertainty in the measurements of the position of the electron.
p.7
Davisson-Germer Experiment and Evidence of Matter Waves
How is the angle of the target adjusted in the experiment?
The target is rotated about an angle along the direction of the beam.
p.10
Wave-Particle Duality and Quantum Theory
What is the significance of substituting ω = 2πν in the wave equation?
It relates angular frequency to frequency.
p.17
Band Theory of Solids and Electron Theory
What is a drawback of classical free electron theory regarding energy absorption?
It states that all free electrons absorb the supplied energy, while quantum theory states that only a few do.
p.6
De Broglie's Concept of Matter Waves
What is the formula for the de-Broglie wavelength of an electron?
𝜆 = h / √(2mE), where h = 6.626 x 10^-34 Js, m = 9.1 x 10^-31 Kg, and e = 1.6 x 10^-19 C.
p.20
Schrodinger's Wave Equation and Particle in a Box
What is the form of the Schrödinger's equation for the region where 0 < x < a?
0 = (d²ψ/dx²) + (2m/ħ²)Eψ.
p.15
Band Theory of Solids and Electron Theory
What is the role of free electrons in the classical free electron theory?
They are responsible for electrical conduction.
p.19
Schrodinger's Wave Equation and Particle in a Box
What is the equation representing the periodic potential in the context of quantum mechanics?
V(x) = V(x + a), where 'a' is the lattice constant.
p.18
Band Theory of Solids and Electron Theory
What is the formula for electrical conductivity?
σ = Q / (t * A * E) = J / E
p.18
Band Theory of Solids and Electron Theory
What is Fermi energy?
The energy of the state at which the probability of electron occupation is ½ at any temperature above 0K; it is the maximum energy of filled states at 0K.
p.17
Band Theory of Solids and Electron Theory
What is relaxation time (τ)?
The average time taken by a free electron to reach its equilibrium position from a disturbed position due to an external electric field, approximately 10^-14 seconds.
p.1
Introduction to Quantum Physics
What are some phenomena that classical theories could not explain?
Compton Effect, Photoelectric Effect, Zeeman Effect, black body radiation.
p.12
Schrodinger's Wave Equation and Particle in a Box
What is the form of the wave function inside the box?
ψ(x) = A sin(Kx) + B cos(Kx).
p.12
Schrodinger's Wave Equation and Particle in a Box
What does the infinite potential energy outside the box imply?
The particle cannot escape from the box.
p.13
Schrodinger's Wave Equation and Particle in a Box
What is the significance of the wave function normalization?
It ensures that the total probability of finding the particle is equal to one.
p.3
Planck's Hypothesis and Radiation Law
How does the frequency of radiation relate to the vibrating particles in Planck's theory?
The frequency of radiation is the same as that of the vibrating particles.
p.19
Wave-Particle Duality and Quantum Theory
What is the form of the solution to Schrödinger's equation proposed by Bloch?
Ψₖ(x) = e^(±ikx) Uₖ(x), known as the Bloch function.
p.19
Band Theory of Solids and Electron Theory
What does Uₖ(x) represent in the context of Bloch functions?
A periodic function with the periodicity of the crystal lattice.
p.1
Introduction to Quantum Physics
What was the prevailing belief about physics until the end of the nineteenth century?
Classical physics was considered sufficient for all physical phenomena.
p.9
Heisenberg Uncertainty Principle
What does Δt represent in the Heisenberg Uncertainty Principle?
The error in the measurements of time.
p.7
Davisson-Germer Experiment and Evidence of Matter Waves
What is the target used in the Davisson-Germer experiment?
A large single crystal of nickel.
p.19
Band Theory of Solids and Electron Theory
How did Kronig and Penny modify the potential energy curves for studying electron behavior?
They represented them as rectangular square potential wells.
p.16
Band Theory of Solids and Electron Theory
What is mean free path?
The average distance traveled by a free electron between two successive collisions.
p.3
Planck's Hypothesis and Radiation Law
What observation is made about the energy distribution in the spectrum of a black body?
The distribution of energy is not uniform.
p.1
Black Body Radiation and Kirchhoff's Law
How can a perfect black body be approximated?
By using a cavity with blackened walls, where a small hole behaves like a black body surface.
p.1
Black Body Radiation and Kirchhoff's Law
What does Kirchhoff's law imply about the emissive power of a black body?
It does not depend on the nature of the body, indicating universal properties.
p.3
Planck's Hypothesis and Radiation Law
What are the values of energies in Planck's hypothesis?
0, hν, 2hν, 3hν, ..., nhν.
p.3
Planck's Hypothesis and Radiation Law
What is the significance of the oscillators moving from one state to another in Planck's theory?
They can radiate energy during this transition.
p.11
Schrodinger's Wave Equation and Particle in a Box
What is the equation known as Schrodinger’s time-independent wave equation for one-dimensional motion?
𝜕²ψ/𝜕x² + (2m/ℏ²)(E - V)ψ = 0.
p.4
Wave-Particle Duality and Quantum Theory
What are the characteristic parameters of a particle?
Mass, velocity, momentum, and energy.
p.18
Band Theory of Solids and Electron Theory
What does Bloch's theorem describe?
It describes how conduction electrons move throughout a crystalline lattice composed of ionic cores.
p.11
Schrodinger's Wave Equation and Particle in a Box
What is the relationship between total energy E, potential energy V, and kinetic energy in the context of the equations?
E = V + (½ mv²) or E - V = (½ mv²).
p.8
Heisenberg Uncertainty Principle
What does the Heisenberg Uncertainty Principle state?
The product of uncertainties in position and momentum is equal to ℏ/2π.
p.4
Planck's Hypothesis and Radiation Law
What is the energy of a photon given by?
E = hν, where ν is the frequency of radiation.
p.16
Band Theory of Solids and Electron Theory
What is collision time?
The average time taken by a free electron between two successive collisions.
p.3
Planck's Hypothesis and Radiation Law
What happens to the intensity of radiation for a particular temperature as wavelength increases?
It increases up to a particular wavelength and then decreases.
p.3
Planck's Hypothesis and Radiation Law
What occurs to the peak energy as temperature increases?
The peak energy shifts towards shorter wavelengths.
p.6
De Broglie's Concept of Matter Waves
How is the wave velocity 'u' of matter waves obtained?
From the photon energy as u = frequency x wavelength.
p.6
De Broglie's Concept of Matter Waves
What is the relationship between particle velocity and de-Broglie wavelength?
Lesser the velocity of the particle, longer the wavelength associated with it.
p.6
De Broglie's Concept of Matter Waves
What is the speed relationship of matter waves compared to the speed of light?
Matter waves travel faster than the velocity of light, but the particle velocity cannot exceed the speed of light.
p.11
Schrodinger's Wave Equation and Particle in a Box
How is the wave function ψ used in quantum mechanics?
It is considered as probability amplitude to find the location of the particle.
p.12
Schrodinger's Wave Equation and Particle in a Box
What happens to the wave function outside the box?
The wave function is zero (|ψ|² = 0 for 0 > x > L).
p.18
Band Theory of Solids and Electron Theory
What are the demerits of quantum free electron theory?
It fails to distinguish between metals, semiconductors, and insulators, and does not explain the positive value of Hall coefficient and some transport properties of metals.
p.12
Schrodinger's Wave Equation and Particle in a Box
What equation describes the motion of the electron in the one-dimensional box?
The Schrödinger wave equation.
p.2
Rayleigh-Jeans Law and Energy Distribution
What did Rayleigh and Jeans suggest about electromagnetic radiation?
It is caused by the constant absorption and emission of radiation by atoms in the wall of the cavity.
p.2
Rayleigh-Jeans Law and Energy Distribution
What concepts explain the energy distribution in black body radiation?
Stefan’s fourth power law, Wien’s law, and Rayleigh-Jeans law.
p.17
Band Theory of Solids and Electron Theory
What is a key assumption of quantum free electron theory regarding electron movement?
Electrons move in a constant potential within the crystal.
p.15
Band Theory of Solids and Electron Theory
What surrounds the positively charged nucleus in an atom?
Negatively charged electrons.
p.16
Band Theory of Solids and Electron Theory
What did Drude assume about electrons in a metal?
That they are free to move and form an electron gas.
p.12
Schrodinger's Wave Equation and Particle in a Box
What is the potential energy of the particle inside the one-dimensional box?
Zero (V = 0 for 0 < x < L).
p.13
Schrodinger's Wave Equation and Particle in a Box
What happens to the wave function ψ when x = L?
ψ = 0, which implies ψ² = 0.
p.8
De Broglie's Concept of Matter Waves
What is Bragg's equation used for in this context?
To calculate the wavelength from diffraction patterns.
p.10
Schrodinger's Wave Equation and Particle in a Box
What does the equation ∂²ψ/∂t² = -ω²ψ represent?
The relationship between time and wave displacement in wave mechanics.
p.11
Schrodinger's Wave Equation and Particle in a Box
What does ℏ represent in the equations?
ℏ = h/2π, where h is Planck's constant.
p.16
Band Theory of Solids and Electron Theory
What happens to electrons when an external electric field is applied?
They acquire energy and move towards the positive potential, resulting in drift velocity.
p.17
Band Theory of Solids and Electron Theory
Who proposed the quantum free electron theory and when?
Somerfield proposed it in 1928.
p.20
Schrodinger's Wave Equation and Particle in a Box
What does the equation abmVo = P represent?
It relates the potential energy of the barrier to the wave function parameters.
p.14
Schrodinger's Wave Equation and Particle in a Box
What does the figure mentioned illustrate?
The energy level diagram for the particle.
p.10
Schrodinger's Wave Equation and Particle in a Box
What is the result of differentiating the wave function with respect to time?
∂²ψ/∂t² = -ω²ψ₀(x)e^{-iωt}.
p.1
Black Body Radiation and Kirchhoff's Law
What is black body radiation considered in quantum physics?
The first theory of quantum physics.
p.7
Davisson-Germer Experiment and Evidence of Matter Waves
What device is used to detect scattered electrons in the experiment?
A Faraday cylinder connected to a galvanometer.
p.8
Heisenberg Uncertainty Principle
What are the two physical quantities described by the Heisenberg Uncertainty Principle?
Position (Δx) and momentum (Δp).
p.4
De Broglie's Concept of Matter Waves
What concept did de Broglie suggest in 1924?
That particles like electrons exhibit wave-like properties.
p.13
Schrodinger's Wave Equation and Particle in a Box
What are the integer values n known as?
Quantum numbers of energy levels Eₙ.
p.20
Wave-Particle Duality and Quantum Theory
What does the term 'K' represent in the wave function?
K is the propagation vector, K = 2π/λ, where λ is the de Broglie wavelength of the electron.
p.17
Band Theory of Solids and Electron Theory
What is one merit of classical free electron theory?
It is used to verify Ohm’s law.
p.18
Band Theory of Solids and Electron Theory
How is the potential energy of a conduction electron in a lattice characterized?
It is minimum at the positive ion sites and maximum between the two ions.
p.7
Davisson-Germer Experiment and Evidence of Matter Waves
What is the significance of the 'bump' observed in the galvanometer current?
It indicates the diffraction pattern of electrons, supporting the wave nature of matter.
p.13
Schrodinger's Wave Equation and Particle in a Box
What does the spacing between energy levels depend on?
The spacing increases as (2n + 1)E₁.
p.3
Planck's Hypothesis and Radiation Law
What is the nature of energy radiation according to Planck's theory?
The radiation of energy is discrete, not continuous.
p.6
De Broglie's Concept of Matter Waves
What does it mean when v = 0 in terms of de-Broglie wavelength?
When v = 0, λ = ∞, indicating that matter waves are generated by the motion of particles.
p.16
Band Theory of Solids and Electron Theory
What happens to valence electrons when atoms are brought closer to form a metal?
They get detached and move freely through the metal.
p.2
Stefan-Boltzmann Law and Wien's Law
What happens to λm when the temperature of the black body increases?
λm shifts towards the minimum value.
p.17
Band Theory of Solids and Electron Theory
How does classical free electron theory explain the conductivity of metals?
It explains the electrical and thermal conductivity of metals.
What did G.R. Kirchhoff prove in 1959 regarding black body radiation?
The ratio of emissive power to absorption coefficient is the same for all bodies at the same temperature.
p.1
Black Body Radiation and Kirchhoff's Law
What is a black body defined as?
A body that absorbs all radiant energy falling upon it and emits all wavelengths of radiation when heated.
p.15
Band Theory of Solids and Electron Theory
What are the three types of conducting materials based on conductivity?
Zero resistivity, low resistivity, and high resistivity materials.
p.15
Band Theory of Solids and Electron Theory
What does the Electron Theory of Solids explain?
The structure and properties of solids through their electronic structure.
p.3
Planck's Hypothesis and Radiation Law
What did Planck suggest in 1900 to explain the energy distribution in black body radiation?
He proposed a new hypothesis regarding discrete energy oscillations of electrons.
p.15
Band Theory of Solids and Electron Theory
What does the quantum free electron theory obey?
The laws of quantum mechanics.
p.20
Schrodinger's Wave Equation and Particle in a Box
What is the relationship derived from differentiating the wave function and substituting into the Schrödinger's equations?
ka = αa + αa * cos(2mVo/ħ²) * sin(αa).
p.4
Wave-Particle Duality and Quantum Theory
What are the characteristics of waves?
Amplitude, time period, frequency, wavelength, phase, and intensity.
p.15
Band Theory of Solids and Electron Theory
What determines the conducting property of a solid?
The number of valence electrons.
p.2
Rayleigh-Jeans Law and Energy Distribution
What is the average energy (ε) of oscillators in thermal equilibrium according to classical statistical mechanics?
ε = KT/2, where K is Boltzmann’s constant.
p.15
Band Theory of Solids and Electron Theory
What is the classical free electron theory based on?
The movement of electrons in a lattice obeying classical mechanics.
p.20
Schrodinger's Wave Equation and Particle in a Box
What is the form of the Schrödinger's equation for the region where -b < x < 0?
0 = (d²ψ/dx²) - (2m/ħ²)(Vo - E)ψ.
p.6
De Broglie's Concept of Matter Waves
Are matter waves electromagnetic waves?
No, matter waves are not electromagnetic waves; they are pilot waves guiding the particle.
p.13
Schrodinger's Wave Equation and Particle in a Box
What does the equation KL = nπ represent?
It represents the quantization condition for the wave function in a box.
p.7
Davisson-Germer Experiment and Evidence of Matter Waves
What is observed in the galvanometer current as the angle is varied?
A 'bump' begins to appear in the curve for certain acceleration potentials.
p.10
Schrodinger's Wave Equation and Particle in a Box
What does the equation ∂²ψ/∂x² = -k²ψ represent?
The wave equation in terms of spatial displacement.
p.17
Band Theory of Solids and Electron Theory
What phenomenon cannot be explained by classical free electron theory?
The photoelectric effect, Compton effect, and blackbody radiation.
p.17
Band Theory of Solids and Electron Theory
What is the experimental value of specific heat of a metal compared to classical theory?
Classical theory predicts 4.5R, while the experimental value is 3R.
p.3
Planck's Hypothesis and Radiation Law
What assumption did Planck make about the particles in a black body?
They are oscillating particles that can vibrate at all possible frequencies.
p.20
Schrodinger's Wave Equation and Particle in a Box
What are the widths of the potential well and potential barrier in the model?
The width of the potential well is 'a' and the potential barrier is 'b'.
p.13
Schrodinger's Wave Equation and Particle in a Box
What is the lowest energy of the particle in the box?
E₁ = (ħ²π²)/(2mL²), known as zero point energy.
p.13
Schrodinger's Wave Equation and Particle in a Box
How are the energy levels of the particle in the box quantized?
The energy levels are discrete and given by Eₙ = n²E₁.
p.20
Schrodinger's Wave Equation and Particle in a Box
What equations are used to calculate the energies and wave functions of the electron?
The time-independent one-dimensional Schrödinger’s wave equations.
p.6
De Broglie's Concept of Matter Waves
What happens to the de-Broglie wavelength as the mass of the particle decreases?
The lighter the particle, the greater the wavelength associated with it.
p.20
Schrodinger's Wave Equation and Particle in a Box
What does the equation (x) u e = ψ(x) represent?
It represents the wave function of the electron in the potential well and barrier.
