ch 301 lecture 1
Rutherford model and the limits of classical mechanics
Atoms visualized as planetary systems: a small, dense nucleus with electrons orbiting around it (Rutherford model).
This model is very popular in culture and even used as a symbol by some government-related contexts (the speaker mentions a government agency with energy in its name using this symbol).
The Rutherford/planetary picture is not actually correct; atoms are more complicated than a simple nucleus with freely orbiting electrons.
Classical mechanics (Newtonian picture: F = ma, laws of motion) explained macroscopic motion well (e.g., getting to the Moon in the 1960s) but failed for atoms.
Why classical mechanics fails for atoms:
Electrons are charged and would radiate energy when accelerated in circular orbits, causing them to lose energy and spiral into the nucleus (instability). The observed stability of atoms contradicts simple classical predictions.
The full atomic behavior involves interactions that Newtonian mechanics can’t capture alone; this pushed the development of quantum concepts.
The lecture audience is assumed to have a high school chemistry background, and readiness materials are used to bridge gaps.
The session emphasizes reconciling the classical picture with observed atomic behavior before introducing quantum ideas.
Light, waves, and electromagnetic radiation (EMR)
Light as electromagnetic radiation: composed of oscillating electric and magnetic fields perpendicular to each other and to the direction of travel.
Waves propagate through space; light travels at the speed of light, c = 3 imes 10^{8}\ \mathrm{m\,s^{-1}}.
Wave terminology:
Wavelength \lambda: distance between identical points on successive cycles (e.g., peak to peak or trough to trough).
Frequency \nu (nu): number of cycles per second, measured in hertz (Hz, s^{-1}).
Amplitude: height of the wave; relates to brightness/intensity (larger amplitude = brighter; smaller amplitude = dimmer).
Relationship between wavelength and frequency:
\nu = \frac{c}{\lambda}
Equivalently, \lambda = \frac{c}{\nu}
Units and practical notes:
Frequency: s^{-1} (Hz); often described in kilohertz, megahertz, gigahertz, etc.
Wavelength units: meters or nanometers (nm). 1 meter = 10^9 nanometers; 1 nm = 10^{-9} m.
The visual and everyday relevance of light:
Light enables sight; interaction with matter depends on wave properties and energy.
All kinds of devices exploit EMR (e.g., phones, Bluetooth, sensing devices).
The speaker emphasizes not worrying about every detailed symbol on the board; focus on core relations and definitions.
Oscilloscope-like amplitudes: amplitude relates to the height of the waveform and associated intensity/brightness; devices (e.g., oscilloscopes) show amplitude in units depending on the measurement context.
Quick-note on notation:
c on the speed-of-light term is the same constant used across frequency/wavelength relations; formulas are interchangeable depending on what you’re solving for (frequency or wavelength).
The electromagnetic spectrum (EMR)
The EMR spectrum is ranked by frequency (left) and wavelength (bottom).
Frequency axis covers from about 10^{4} to 10^{24} Hz; wavelength axis covers from about 10^{5} to 10^{-15} m.
Inverse relationship: higher frequency implies shorter wavelength and vice versa.
Regions of the spectrum (with qualitative effects and common uses):
Radio waves: low energy; used for listening devices, Bluetooth, communications; MRI uses radio waves to interact with nuclear spins.
Microwaves: can affect electron spins and rotate water molecule vibrations; heating food via water molecule heating.
Infrared: perceived as heat; emitted by nearly all warm objects; you sense infrared as thermal radiation.
Visible light: the narrow band the human eye can perceive; the spectrum of visible light is often remembered via the Roy G. Biv mnemonic (Red, Orange, Yellow, Green, Blue, Indigo, Violet).
Ultraviolet: higher energy; can cause skin damage (sunburn, skin cancer) with excessive exposure.
X-rays: higher energy; capable of exciting core electrons; used in medical imaging and material analysis.
Gamma rays: very high energy; originate from nuclear decay and cosmic sources; highly penetrating and hazardous.
Practical advice from the lecturer:
Memorize the regions and their general effects; the review notes contain the detailed ranges and implications.
Use nanometers (nm) for wavelength ranges in the visible/near-IR/near-UV to keep numbers simple; 1 nm = 10^{-9} m.
The review notes (Canvas) are the primary resource for the specific ranges and the mnemonics.
The review notes introduce the term EMR (electromagnetic radiation) and emphasize their relevance to understanding matter interactions.
Energy, Planck’s constant, and photon energy
Planck’s constant: h \approx 6.626 \times 10^{-34}\ \mathrm{J\,s}. The lecture also uses a simplified value of about 7 \times 10^{-34}\ \mathrm{J\,s} for ease of calculation.
Photon energy: E = h\nu = \frac{h c}{\lambda}. This relates the energy of a photon to either its frequency or its wavelength.
Example calculation (illustrative): given energy E = 3 \times 10^{-19}\ \mathrm{J},
With h \approx 7 \times 10^{-34}\ \mathrm{J\,s} and c = 3 \times 10^{8}\ \mathrm{m\,s^{-1}}:
Frequency: \nu = \frac{E}{h} \approx \frac{3\times 10^{-19}}{7\times 10^{-34}} \approx 4.3\times 10^{14}\ \mathrm{s^{-1}}.
Wavelength: \lambda = \frac{h c}{E} \approx \frac{(7\times 10^{-34})(3\times 10^{8})}{3\times 10^{-19}} \approx 7\times 10^{-7}\ \mathrm{m} = 700\ \mathrm{nm}.
Important practical note:
The numbers are often rounded for teaching convenience; exact constants produce very close results (e.g., a true value around a few hundred nm differs slightly from 700 nm but is acceptable for introductory problems).
Energy units and interconversion:
Energy can be expressed in joules or electron volts (eV). 1 eV ≈ 1.602 × 10^{-19} J.
When solving problems, you may be asked to convert between E, \nu, and \lambda; algebraic manipulation is sufficient because formula sheets are provided on quizzes/exams.
Wave-particle duality and the photoelectric effect
Light exhibits wave-like and particle-like properties (wave-particle duality).
Photon concept: a packet of light that carries energy E_{\text{photon}} = h\nu = \frac{h c}{\lambda}. The energy of a photon must reach a threshold to cause electron emission in the photoelectric effect.
Work function (threshold energy) \phi (often called the work function of the surface):
An electron is ejected only if the photon energy is at least E_{\text{photon}} \ge \phi. If not, no current is produced.
If emission occurs, the excess energy becomes kinetic energy: K.E. = E_{\text{photon}} - \phi. This explains why emission occurs only above threshold and why kinetic energy increases with photon energy.
Einstein’s photoelectric effect and Nobel Prize: Einstein explained the particle nature of light via the photoelectric effect, which earned him the Nobel Prize (often associated with E = mc^2 in popular references, but the prize was for the photoelectric effect).
Worked example (metal surface):
Photon energy chosen as E_{\text{photon}} = 2.48\ \text{eV}; surface work function \phi = 2.36\ \text{eV}.
Threshold: since 2.48 > 2.36\ \text{eV}, electrons are emitted; kinetic energy per electron is K.E. = (2.48 - 2.36)\ \text{eV} = 0.12\ \text{eV}.
Convert to joules if needed: 0.12\ \text{eV} \approx 0.12 \times 1.602\times 10^{-19}\ \mathrm{J} \approx 1.92\times 10^{-20}\ \mathrm{J}.
Polling example from the lecture: given a photon energy of 2.48\ \text{eV} and work functions for several metals (Li, Be, Na, Al), only sodium (Na) will yield a current because its work function is lower than the photon energy (phi ≈ 2.36 eV in the example).
Takeaway: The photoelectric effect demonstrates quantization of light energy and the necessity of a threshold energy for electron emission, reinforcing the quantum picture of light as consisting of photons.
Worked example: interconversion and problem-solving steps
Given energy and asked for wavelength: use \lambda = \frac{h c}{E}. Steps:
1) Substitute values for h, c, and the given energy E.
2) Compute the numerator h c and then perform the division by E.
3) Convert to preferred units if needed (e.g., meters to nanometers: 1\ \mathrm{m} = 10^{9}\ \mathrm{nm}).Example recap (re-stating the earlier calculation): with E = 3 \times 10^{-19}\ \mathrm{J},
\nu = \frac{E}{h} \approx \frac{3\times 10^{-19}}{7\times 10^{-34}} \approx 4.3\times 10^{14}\ \mathrm{s^{-1}}.
\lambda = \frac{h c}{E} \approx \frac{(7\times 10^{-34})(3\times 10^{8})}{3\times 10^{-19}} \approx 7\times 10^{-7}\ \mathrm{m} = 700\ \mathrm{nm}.
In addition to wavelength-energy conversions, the lecture emphasizes that you can switch between forms depending on what you’re solving for (e.g., if you need frequency, use \nu = E/h; if you need wavelength, use \lambda = h c / E). The formula sheets provided in quizzes/exams will include the necessary variations.
Summary of key concepts and connections
Atom structure began with a Rutherford-like model but classical physics could not explain atomic stability or spectral lines; this led to quantum ideas.
Light is both a wave and a particle: a fundamental duality that explains phenomena like interference and the photoelectric effect.
Photons carry energy E_{\text{photon}} = h\nu = \dfrac{h c}{\lambda}; the energy required to eject an electron from a surface is the work function \phi.
If E{\text{photon}} < \phi, no emission occurs; if E{\text{photon}} \ge \phi, electrons are ejected with kinetic energy K.E. = E_{\text{photon}} - \phi.
The electromagnetic spectrum provides a framework for understanding how different wavelengths and frequencies interact with matter, with practical applications in imaging, heating, communications, and spectroscopy.
The math behind these concepts is interconvertible via \nu = c/\lambda and E = h\nu = hc/\lambda, with Planck’s constant h as the bridge between energy and frequency.
Throughout, the emphasis is on using the provided formula sheets and understanding how to manipulate equations algebraically rather than memorizing every constant value exactly; rounding is permitted for teaching purposes, and precision is improved in real calculations as needed.
Quick references for recall
Key equations:
E = h \nu
E = \dfrac{h c}{\lambda}
\nu = \dfrac{c}{\lambda}
\lambda = \dfrac{h c}{E}
K.E. = E_{\text{photon}} - \phi
Important constants:
c = 3 \times 10^{8}\ \mathrm{m/s}
h \approx 6.626 \times 10^{-34}\ \mathrm{J\,s} (teaching value used: ≈ 7 \times 10^{-34}\ \mathrm{J\,s} for simplified calculations)
Notation:
\phi: work function / threshold energy for electron emission
E_{\text{photon}} = h\nu = hc/\lambda
1\ \text{eV} = 1.602 \times 10^{-19}\ \mathrm{J}.