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Flashcards · AP® Physics 2: Algebra-Based · Unit 15

Unit 15: Modern Physics flashcards

55 cards on topics 15.1 to 15.8. Pick a topic or study the whole unit.

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15.1 Quantum Theory and Wave-Particle Duality

Why was quantum theory developed?
Classical physics could not explain atomic spectra, blackbody radiation or the photoelectric effect. Quantum theory is needed at atomic and subatomic scales.
What is a photon, and what is its energy?
A massless, neutral quantum of light with energy E = hf = hc/λ, where h = 6.63 × 10⁻³⁴ J·s = 4.14 × 10⁻¹⁵ eV·s and λ is the vacuum wavelength. 1 eV = 1.60 × 10⁻¹⁹ J.
What is the energy of a 620 nm photon?
E = hc/λ ≈ 3.21 × 10⁻¹⁹ J, which is about 2.0 eV (1240 eV·nm ÷ 620 nm).
Does brighter light mean higher-energy photons?
No. Frequency sets the energy of each photon; intensity sets the number of photons per second (N/t = P/E).
What is the de Broglie wavelength?
Every particle has λ = h/p = h/(mv). Heavier or faster particles have shorter wavelengths. Doubling the momentum halves λ.
What is wave-particle duality?
In a dim two-slit experiment each photon or electron arrives as one dot, but many dots build up an interference pattern. The wave describes where a particle is likely to be detected.
When are wave effects of particles noticeable?
Only when the de Broglie wavelength is comparable to the size of the system, such as an electron (λ about 10⁻¹⁰ m) passing through atomic spacings.
Does a photon's energy change when light enters glass?
No. Its speed becomes c/n and its wavelength λ/n, but the frequency, and so the photon energy, is unchanged.

15.2 The Bohr Model of Atomic Structure

What is the structure of an atom?
A tiny positive nucleus of protons and neutrons holding almost all the mass, surrounded by electrons (about 1/1800 of a proton's mass). Most of the atom is empty space.
How do you read nuclear notation such as ¹⁸₈O²⁻?
Top left is the mass number A (18), bottom left the atomic number Z (8 protons). Neutrons N = A − Z = 10. A 2− ion has 2 more electrons than protons: 10.
What is the difference between an isotope and an ion?
Isotopes of an element have the same Z but different numbers of neutrons (different A). An ion has a net charge because its protons and electrons differ. Only Z decides the element.
What sets the allowed orbits in the Bohr model?
Only orbits whose circumference holds a whole number of de Broglie wavelengths: 2πr = nλ. So only certain radii and energies are allowed.
What are the energy levels of hydrogen in the Bohr model?
E = −13.6 eV/n², with zero at infinite separation. The ground state (n = 1) is the most negative level, not zero.
How do radius and speed change between hydrogen's n = 1 and n = 2 orbits?
r = n²r₁, so r is 4 times larger (2.12 × 10⁻¹⁰ m). v = v₁/n, so the speed halves. Electrons in bigger orbits are slower.

15.3 Emission and Absorption Spectra

How does an atom emit a photon?
An excited atom drops spontaneously to a lower state and emits one photon with E_photon = |E_upper − E_lower|. One transition gives one frequency, so atoms produce line spectra.
When can an atom absorb a photon?
For a jump between bound states, only if the photon energy exactly matches a gap. Any photon at or above the binding energy can ionize the atom instead.
What is the quick link between photon energy and wavelength?
λ (nm) ≈ 1240 ÷ E (eV), since hc ≈ 1.24 × 10³ eV·nm. A 4.0 eV photon has λ ≈ 310 nm (ultraviolet). Bigger gap: higher f, shorter λ.
What is the difference between emission and absorption spectra?
Emission: bright lines from a hot, low-density gas. Absorption: dark lines in a continuous spectrum after light crosses a cooler gas. A cool gas shows fewer lines because its atoms start in the ground state.
How many emission lines can an atom with five energy levels produce?
N(N − 1)/2 = 5 × 4 ÷ 2 = 10.
What is binding energy for an electron in an atom?
The energy needed to free the electron from a given state: 0 − E_n. It is largest from the ground state. A freed electron has K = E_photon − binding energy.
How are spectra used to identify elements?
Each element has its own energy levels, so its own pattern of lines. Match the whole pattern, not a single line.

15.4 Blackbody Radiation

What is a blackbody?
An object that absorbs all radiation falling on it. At constant temperature it emits at the same rate as it absorbs, with a continuous spectrum that depends only on temperature.
What is Wien's law?
λ_max = b/T, with b = 2.898 × 10⁻³ m·K and T in kelvin. Peak wavelength is inversely proportional to temperature: 2900 K peaks near 1.0 μm (infrared).
How much power does a blackbody emit?
P = σAT⁴, with σ = 5.67 × 10⁻⁸ W/(m²·K⁴) and T in kelvin. Tripling T multiplies the power by 3⁴ = 81.
How do blackbody curves change with temperature?
A hotter curve is higher at every wavelength (curves never cross) and peaks at a shorter wavelength. The area under the curve is the power per unit area.
What was the ultraviolet catastrophe?
Classical physics predicted ever-rising emission at short wavelengths. Planck's law fitted the data by assuming light energy is emitted in quanta, E = hf.
Why do hot objects change colour as they heat up?
The peak moves to shorter wavelengths, so they glow dull red, then brighter, then white. Bluish stars are hotter than reddish ones.

15.5 The Photoelectric Effect

What is the photoelectric equation?
K_max = hf − φ, where φ is the work function (minimum energy to remove an electron). Use the same unit (J or eV) throughout.
What is the threshold frequency?
f₀ = φ/h, the minimum frequency for emission; the threshold wavelength is λ₀ = hc/φ. Below f₀ no electrons are emitted however bright the light; emission needs λ shorter than λ₀.
Why is the photoelectric effect evidence for photons?
K_max depends on frequency, not intensity, and there is a threshold frequency. One electron absorbs one photon's energy; it cannot save up energy from several photons.
The intensity of light on a photoactive metal is tripled. What happens?
K_max is unchanged; about three times as many electrons are emitted each second, so the current triples.
What does a graph of K_max against frequency show?
A straight line with slope h (the same for every material), horizontal intercept f₀ and extended vertical intercept −φ. It does not pass through the origin.
What is the stopping potential?
The potential difference that just stops the fastest electrons: eV_s = K_max. K_max in eV equals V_s in volts.
Light of 300 nm falls on a metal with φ = 3.10 eV. What is K_max?
E = 1240 ÷ 300 ≈ 4.13 eV, so K_max = 4.13 − 3.10 = 1.03 eV.

15.6 Compton Scattering

What is Compton scattering?
A photon (usually an X-ray) collides with a free electron at rest and scatters at an angle θ. It gives the electron some energy, so it leaves with lower energy and a longer wavelength.
What is the Compton shift formula?
Δλ = (h/m_e c)(1 − cos θ), with h/(m_e c) = 2.43 × 10⁻¹² m. Δλ is 0 at 0°, 2.43 pm at 90° and 4.85 pm (the maximum) at 180°.
Does the Compton shift depend on the starting wavelength?
No. Δλ depends only on the angle. A shorter-wavelength photon loses a larger fraction of its energy for the same shift.
Why is Compton scattering evidence for photons?
A classical wave model predicts no change in wavelength. Treating the photon as a particle with momentum p = h/λ that obeys energy and momentum conservation explains the shift.
Does a scattered photon slow down?
No. Its speed stays c; it loses energy, so its wavelength increases. Photon momentum is p = h/λ = E/c, not mv.
How is energy shared in Compton scattering?
hc/λ = hc/λ′ + K_e: the photon's energy loss becomes the electron's kinetic energy. Momentum components are also conserved, so the electron recoils on the other side of the axis from the photon.

15.7 Fission, Fusion, and Nuclear Decay

What is the difference between fission and fusion?
Fusion: small nuclei join into a larger one. Fission: a heavy nucleus splits into smaller nuclei, usually with neutrons. Both release energy when the products have higher binding energy per nucleon (peak near iron).
How do you balance a nuclear equation?
Nucleon number A and charge number Z are each conserved. For ¹₀n + ²³⁵₉₂U → ¹⁴¹₅₆Ba + ⁹²₃₆Kr, the missing products are 3 ¹₀n.
How do you find the energy released by a nuclear reaction?
Q = Δm c², from the mass decrease. Using 1 u = 931 MeV/c², a loss of 0.0100 u releases 9.31 MeV. Mass is not conserved; nucleon number is.
What fraction of a radioactive sample is left after three half-lives?
(½)³ = ⅛. Two half-lives leave ¼, not zero. In general N = N₀(½)^(t/t½) = N₀e^(−λt).
How are the decay constant and half-life related?
λ = ln 2 / t½. A half-life of 10 s gives λ ≈ 0.0693 s⁻¹. Keep time units consistent.
Is radioactive decay predictable?
For one nucleus it is random. For a large sample, probability makes the number left very close to the predicted value.
What is the strong force?
The force between nucleons. It dominates at nuclear distances (about 10⁻¹⁵ m) and is negligible beyond a few of those distances.
How is kinetic energy shared between two products from a nucleus at rest?
Momentum is conserved, so they have equal and opposite momenta and K ∝ 1/m: the lighter product gets more kinetic energy.

15.8 Types of Radioactive Decay

What happens to A and Z in alpha decay?
A falls by 4 and Z by 2: the nucleus emits ⁴₂He, a helium-4 nucleus (2 protons + 2 neutrons, charge +2e). ²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He.
What happens in β⁻ decay?
A neutron becomes a proton in the nucleus, emitting an electron and an antineutrino. A is unchanged and Z rises by 1. The electron is created in the nucleus, not taken from the shells.
What happens in β⁺ decay?
A proton becomes a neutron, emitting a positron (electron mass, charge +e) and a neutrino. A is unchanged and Z falls by 1.
What is gamma decay?
An excited nucleus left by an alpha or beta decay drops to a lower energy state and emits a photon. A and Z are unchanged, so the element stays the same.
Why do beta particles have a range of energies but alpha particles do not?
In beta decay three particles share the energy (including the neutrino or antineutrino). In alpha decay only two share it, so the alpha energy is fixed for each final state.
Why do neutrinos pass through Earth almost untouched?
They have no charge and negligible mass, and interact only through the weak force and gravity.
How is lepton number conserved in beta decay?
e⁻ and ν have lepton number +1; e⁺ and ν̄ have −1. So e⁻ is emitted with ν̄, and e⁺ with ν, keeping the total at zero.

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