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Physics – Modern Physics

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    Study Guide Physics – Modern Physics 1. Quantum Mechanics Classical physics works well for everyday objects, but it fails in two major areas: • Objects moving close to the speed of light • Matter at the atomic and subatomic scale To understand how atoms, molecules, and nuclei behave, scientists developed quantum mechanics . This branch of physics explains phenomena that classical mechanics cannot. 1. Blackbody Radiation A blackbody is an ideal object with two special properties: • It absorbs all radiation that falls on it. • It emits radiation perfectly when heated. When scientists studied how the intensity of radiation varies with wavelength, they found that classical physics could not explain the results . 2. Planck’s Solution In 1900, Max Planck proposed a revolutionary idea. To match experimental data, he made two key assumptions: 1. Energy is quantized Molecules can only have specific energy values, not any value. These energy levels are given by: [E = hf] where:

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    Study Guide ○ (n) is a quantum number (1, 2, 3, …) ○ (f) is frequency 2. Energy is emitted in packets Energy is released in small bundles called quanta , now known as photons . The energy of each photon is: [E = hc/λ] Why This Was Important This idea was radical because it treated energy as discrete packets instead of a smooth, continuous flow. A molecule can only change its energy if it absorbs or emits exactly one quantum of energy. 3. Photoelectric Effect The photoelectric effect occurs when light shines on certain metals and causes electrons to be ejected. These electrons are called photoelectrons . Scientists noticed several surprising results: • Each metal requires a minimum frequency of light, called the threshold (cutoff) frequency • Increasing light intensity does not increase the electrons’ kinetic energy

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    Study Guide • Increasing light frequency increases the electrons’ maximum kinetic energy • Electrons are emitted almost instantly , even at low intensities 4. Einstein’s Explanation Albert Einstein explained the photoelectric effect using Planck’s quantum idea and energy conservation. He proposed the equation: [K.E. max = hf – Q] Where: • (hf) is the energy of the incoming photon • (Q) is the work function (minimum energy needed to remove an electron from the metal) What This Means • If the photon energy is less than (Q) → no electrons are emitted • Extra photon energy becomes kinetic energy of the electron 5. Explaining the Observations • A threshold frequency is required because each photon must carry enough energy • Higher intensity means more photons → more electrons, but same kinetic energy • Higher frequency means more energetic photons → faster electrons • Even low - intensity light can eject electrons immediately if frequency is high enough

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    Study Guide 6. Compton Scattering More evidence for quantum behavior came from the Compton effect , discovered by Arthur Compton . In this effect: • A high - energy X - ray photon collides with an electron • The scattered photon loses energy and gains a longer wavelength This change can be explained only if the photon behaves like a particle with momentum. Key Features • Energy and momentum conservation apply (like billiard - ball collisions) • The wavelength shift depends on the scattering angle • The effect is noticeable only for high - energy photons , such as X - rays 7. Particle – Wave Duality Experiments like the photoelectric and Compton effects show that light behaves as both a wave and a particle . • High - energy photons (short wavelength, e.g. X - rays) behave more like particles • Low - energy photons (long wavelength, e.g. radio waves) behave more like waves Both models are necessary to fully describe electromagnetic radiation. 8. De Broglie Waves Louis de Broglie suggested a bold idea: If light (a wave) can act like a particle, then particles might also behave like waves .

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    Study Guide Important Note • De Broglie wavelengths are extremely small for everyday objects • Because Planck’s constant is very tiny ((10^{ - 34})), wave effects are noticeable only for very small particles like electrons 9. Heisenberg Uncertainty Principle The Heisenberg uncertainty principle states that it is impossible to measure both: • the exact position , and • the exact momentum of a particle at the same time.

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    Study Guide 2. Atomic Structure 1. Quantization of Angular Momentum Bohr proposed that electrons can move only in certain allowed circular orbits around the nucleus. In these orbits, the angular momentum of the electron is quantized, meaning it can take only specific values: Here: • (n) is an integer called the principal quantum number • (h) is Planck’s constant This condition restricts electrons to specific orbits and is a key idea of the Bohr model. 2. Radius of Electron Orbits Bohr calculated the radius of each allowed orbit by equating: • the electrostatic force (from Coulomb’s law), and

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    Study Guide • the centripetal force needed to keep the electron in circular motion This leads to the expression: When (n = 1), the radius is called the Bohr radius . This is the smallest possible orbit in the hydrogen atom. 3. Energy of an Electron in the Hydrogen Atom The total energy of an electron is the sum of: • Kinetic energy , and • Potential energy After substituting values from Bohr’s equations, the total energy depends only on the quantum number (n). 4. Ground State and Ionization Energy • When (n = 1), the electron is in the ground state • The ground - state energy of hydrogen is – 13.6 eV

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    Study Guide This value matches the ionization energy of hydrogen — the energy required to completely remove the electron from the atom. This excellent agreement strongly supported Bohr’s model. 5. Emission of Radiation and Energy Transitions When an electron jumps from a higher energy level to a lower one, it emits a photon. According to Bohr’s second postulate: [hf = E f - E i ] Substituting the energy expressions gives: Using the relation (c = f λ ), this becomes: 6. The Rydberg Constant From the above equation, the Rydberg constant is identified as:

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