Foundations of Quantum Mechanics: 25 flashcards
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1. What is a blackbody?
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An ideal object that absorbs and re-emits all radiation incident on it.
2. What was the ultraviolet catastrophe?
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The classical prediction that blackbody intensity rises without limit at short wavelengths — contradicted by experiment.
3. State Planck's quantum hypothesis.
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Energy is emitted or absorbed in discrete packets called quanta, each of energy $E = h\nu$.
4. What is the value of Planck's constant $h$?
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$h = 6.626 \times 10^{-34}$ J·s
5. What is the energy distribution function?
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A function describing how the radiated intensity from a blackbody varies with wavelength at a given temperature.
6. What is the photoelectric effect?
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The ejection of electrons from a metal surface when light of sufficient frequency strikes it.
7. What is the threshold frequency in the photoelectric effect?
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The minimum frequency of light below which no electrons are emitted, regardless of intensity.
8. What is the work function $\phi$?
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The minimum energy an electron needs to escape from a metal surface.
9. Write the photoelectric equation.
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$K_{max} = h\nu - \phi$
10. What did Compton scattering demonstrate?
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That X-ray wavelength increases after collision with electrons, proving photons carry momentum $p = h/\lambda$.
11. State the de Broglie hypothesis.
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Every particle has an associated wavelength $\lambda = h/p$, where $p$ is its momentum.
12. What did the Davisson-Germer experiment prove?
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It confirmed electron diffraction from a nickel crystal, validating de Broglie's matter-wave hypothesis.
13. What is wave-particle duality?
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Quantum objects exhibit wave or particle behaviour depending on the experiment used to observe them.
14. State the Heisenberg uncertainty principle for position and momentum.
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$\Delta x \cdot \Delta p \geq \hbar/2$
15. What is the energy-time uncertainty relation?
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$\Delta E \cdot \Delta t \geq \hbar/2$
16. What is the physical meaning of $|\Psi|^2$?
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It gives the probability density of finding the particle at a given position.
17. List the mathematical conditions a valid wave function must satisfy.
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It must be continuous, single-valued, finite everywhere, and normalisable.
18. State the normalisation condition for a wave function.
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$\int_{-\infty}^{\infty} |\Psi|^2 \, dx = 1$
19. Why is the wave function itself not directly measurable?
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Only $|\Psi|^2$ has physical meaning as a probability density; $\Psi$ is generally complex-valued.
20. What is $\hbar$ and its value?
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$\hbar = h/2\pi = 1.055 \times 10^{-34}$ J·s, the reduced Planck's constant.
21. Why does classical physics fail for blackbody radiation?
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It assumes continuous energy exchange, predicting infinite intensity at short wavelengths — the ultraviolet catastrophe.
22. Why does intensity not affect electron kinetic energy in the photoelectric effect?
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Intensity increases the number of photons, not the energy per photon; kinetic energy depends only on frequency.
23. What is the momentum of a photon?
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$p = h/\lambda$
24. Give one real-world application of the photoelectric effect.
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Solar cells and photodetectors convert light into electrical signals using the photoelectric effect.
25. Why is the uncertainty principle not a measurement limitation?
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It is a fundamental property of quantum states — a particle genuinely does not have simultaneously sharp position and momentum.
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