Physics Essentials: 16 flashcards

NDT stands for **Non-Destructive Testing**. Its main purpose is to inspect materials, components, or assemblies for defects or discontinuities **without causing damage** to the object being tested.

Ultrasonic NDT works on the principle of **sound wave reflection at interfaces**. High-frequency sound waves (ultrasonic) are sent into a material; when they hit a boundary or a defect (like a crack or void), they reflect back, and the time and intensity of the echoes reveal the location and size of the flaw.

The three major failures are: **Blackbody radiation**, **Photoelectric effect**, and **Compton effect**. Classical physics could not explain these phenomena, paving the way for quantum theory.

Blackbody radiation is the electromagnetic radiation emitted by a perfect blackbody (an object that absorbs all incident radiation) as a function of temperature. Classical physics (Rayleigh-Jeans law) predicted that intensity would increase indefinitely at short wavelengths (the **ultraviolet catastrophe**), which cont…

Planck proposed that energy is emitted or absorbed in discrete packets called **quanta** or **photons**, with energy given by \(E = h\nu\), where \(h\) is Planck’s constant and \(\nu\) is the frequency of radiation. This quantization of energy led to the correct energy distribution function.

The Planck distribution function is: \(u(\nu, T) = \frac{8\pi h \nu^3}{c^3} \frac{1}{e^{h\nu/k_B T} - 1}\), where \(u\) is the energy density per unit frequency, \(h\) is Planck's constant, \(c\) is the speed of light, \(k_B\) is Boltzmann's constant, and \(T\) is the absolute temperature.

The photoelectric effect is the emission of electrons from a metal surface when light of sufficient frequency shines on it. Classical physics expected that higher intensity light would give electrons more energy, but experiments showed that the **maximum kinetic energy** of emitted electrons depends on the **frequency*…

The Compton effect is the increase in wavelength (decrease in energy) of X-rays when they scatter off free electrons. The change in wavelength is given by \(\Delta \lambda = \frac{h}{m_e c}(1 - \cos\theta)\), where \(\theta\) is the scattering angle. This effect demonstrates the **particle nature of electromagnetic rad…

The de Broglie hypothesis states that **all matter exhibits wave-like behavior**. A particle with momentum \(p\) has an associated wavelength \(\lambda = \frac{h}{p} = \frac{h}{mv}\), where \(h\) is Planck's constant, \(m\) is the mass, and \(v\) is the velocity.

Wave-particle duality is the concept that every quantum entity (like photons, electrons) exhibits both **wave-like** and **particle-like** properties. For example, light shows interference (wave) but also photoelectric effect (particle); electrons show diffraction (wave) but also localized impact (particle).

The Davisson-Germer experiment directed a beam of electrons at a nickel crystal and observed a **diffraction pattern** in the reflected electrons. The pattern matched the Bragg diffraction condition for waves, confirming the **wave nature of electrons** and validating de Broglie's hypothesis.

The Heisenberg uncertainty principle states that it is impossible to simultaneously know the exact **position** and **momentum** of a particle. The product of the uncertainties is at least \(\hbar/2\): \(\Delta x \cdot \Delta p \ge \frac{\hbar}{2}\), where \(\hbar = h/(2\pi)\).

The wave function \(\Psi(x,t)\) is a mathematical function that contains all the information about a quantum system. It is a complex-valued function of position and time, and its absolute square \(|\Psi|^2\) gives the **probability density** of finding the particle at a given location and time.

A valid wave function must be: (1) **single-valued** (to give a unique probability), (2) **continuous** and have a continuous first derivative (to satisfy the Schrödinger equation), and (3) **square-integrable** (i.e., \(\int_{-\infty}^{\infty} |\Psi|^2 dx\) is finite, so that the total probability can be normalized to…

Normalization is the process of scaling the wave function so that the total probability of finding the particle somewhere in space is exactly 1: \(\int_{-\infty}^{\infty} |\Psi(x,t)|^2 dx = 1\). It is necessary because the wave function's square represents a probability density, and probabilities must sum to 1.

In pulse-echo ultrasonic testing, a transducer sends a short ultrasonic pulse into the metal. If there is a crack or void, part of the wave reflects back earlier than the back-wall echo. The time difference between the initial pulse, the flaw echo, and the back-wall echo is used to calculate the **depth and size** of t…