Title: ETH_Sem3 / Physik_III / Woche7

Q: What is the photoelectric effect?
A: Light causes negative charge (electrons) to be ejected from a metal plate.

Q: Maximum energy of an electron ejected from a metal plate by the photoelectric effect
A: \[E_{\text{max}} = h\nu - \Phi\]Where \(\Phi\) is called the work function.

Einstein's model to explain the photoelectric effect
Light of frequency \(\nu\) arrives in packets, or "quanta", of energy \(h\nu\), where \(h\) is the Planck's constant. These quanta are called photons. The number of photons that arrive per unit time is proportional to the intensity. Since electrons inside a material is attracted to the atomic nuclei, it takes some minimum energy to "kick" one free. This energy is the work function \(\Phi\). If \(h\nu > \Phi\), then each photon can kick an electron, so the higher the light intensity, the larger the current.

Q: How does a photomultiplier tube look like?
A: What is this?

Q: What is the inverse photoelectric effect?
A: A free electron that is shot back into a material will emit a photon (or more than one if it really has a lot of energy).

Q: What is the maximum frequency and minimal wavelength of photons generated using the inverse photoelectric effect?
A: The maximum frequency is \(h\nu_{\text{max}} = eV_0+\Phi\). However, usually \(\Phi \ll eV_0\), resulting in\[\begin{align} \nu_{\text{max}} &= \frac{eV_0}{h} \\ \lambda_\text{min} &= \frac{hc}{eV_0} \end{align}\]Where \(V_0\) is the voltage used to accelerate the electron.

Q: What is Rayleigh scattering?
A: EM radiation scattered elastically by atoms, meaning that the light has the same frequency before and after the interaction

Q: Rayleigh scattering
\[E_\text{emitted} \propto [...]\]For which frequencies does more light get scattered?
A: \frac{\omega^2eE}{m(\omega^2-\omega_0^2)}\cos(\omega t)
Back Extra: For higher frequencies, as long as the model (of a harmonic oscillator) is still valid.
(Fun fact: the reason the sky is blue is because \(\omega_0\) is typically in the ultraviolet.)

Q: What is Bragg scattering ?
A: The scattering of light from periodic features (usually a crystal lattice)

Q: What is the Bragg condition?
(Explanation and formula)
A: It's the condition for constructive interference for Bragg scattering:\[2d\sin(\theta) = \lambda\]

Q: What is Compton scattering?
A: The scattering of a high frequency photon after an interaction with a charged particle, usually an electron.

Q: Compton scattering
\[\Delta\lambda = [...]\]with \(\lambda_c = [...]\) the [...].
A: \lambda_c (1-\cos(\theta) ); \frac{h}{mc}; compton wavelength

Q: [...]\[\lambda = [...]\]
A: de Broglie wavelength; \frac hp

Q: How does an electron microscope look like and why is it useful?
A: What is this?
Answer for backside:
The de Broglie wavelength of a high-energy electron is very small (~pm). This allows us to use electron scattering to look at very small objects.

Q: Electron microscope
What are the lenses made of and why don't we use x-rays or low-energy gamma rays with similar wavelengths?
A: The lenses are made of EM-fields.
Making lenses for x- or gamma rays is really hard since their refractive indices in most material are almost 1 and we can't use EM-fields since they don't interact with each other.

Q: Why is it problematic if the particle/wave used in a high-energy microscope is too energetic?
A: They would simply destroy the sample, preventing any useful observations.