Quantum Foundations: 30 MCQs with answers

Black body radiation

Classical physics could not explain the observed spectrum of black body radiation, especially at short wavelengths, leading to the ultraviolet catastrophe.

Frequency

Planck proposed that energy is quantized and given by E = hν, where ν is the frequency and h is Planck's constant.

Particles have wave-like properties

De Broglie proposed that all matter exhibits wave-like behavior, with a wavelength given by λ = h/p, where p is momentum.

The minimum energy required to eject an electron

The work function is the minimum energy needed to remove an electron from a metal surface.

Joule-second

Planck's constant relates energy to frequency (E = hν), so its units are energy × time, i.e., joule-second.

Momentum

De Broglie's formula λ = h/p shows that wavelength is inversely proportional to momentum p.

False

The Compton effect demonstrates the particle nature of light, as it involves photon-electron collisions with momentum transfer.

True

De Broglie proposed that every particle has an associated wavelength, given by λ = h/p, showing wave-particle duality.

It predicted infinite energy at short wavelengths, known as the ultraviolet catastrophe.

Classical physics (Rayleigh-Jeans law) predicted that the intensity of black body radiation would increase without bound as wavelength decreases, leading to the 'ultraviolet catastrophe'. This failure prompted Planck's quantum hypothesis.

Energy is directly proportional to frequency.

Planck proposed that energy is quantized and given by $E = h\nu$, where $h$ is Planck's constant and $\nu$ is the frequency, showing a direct proportionality.

Light consists of particles called photons, each with energy $h\nu$.

Einstein extended Planck's idea, proposing that light is made of photons, each carrying energy $h\nu$, which explained the instantaneous emission and frequency dependence in the photoelectric effect.

No electrons are emitted regardless of intensity.

If the photon energy $h\nu$ is less than the work function $\phi$, no electron can overcome the binding energy, so no emission occurs, even with high intensity.

They behave as particles with momentum when scattering off electrons.

The Compton effect shows that X-rays scatter like particles (photons) with momentum, as the wavelength shift depends on the scattering angle, confirming particle nature.

$\lambda = \frac{h}{p}$

De Broglie proposed that every particle has a wavelength given by $\lambda = h/p$, where $h$ is Planck's constant and $p$ is momentum.

Davisson-Germer experiment

The Davisson-Germer experiment observed diffraction of electrons by a nickel crystal, confirming de Broglie's hypothesis of matter waves.

The minimum energy required to eject an electron from a metal surface.

The work function $\phi$ is the minimum energy needed to remove an electron from the metal surface; if photon energy is less than $\phi$, no emission occurs.

$K_{max} = h\nu - \phi$

Einstein's photoelectric equation states that the maximum kinetic energy is the photon energy minus the work function: $K_{max} = h\nu - \phi$.

All matter and light exhibit both wave-like and particle-like properties.

Wave-particle duality is the principle that both light and matter (like electrons) can display both wave and particle characteristics depending on the experiment.

Intensity

Classical wave theory predicted that greater intensity (amplitude) would give electrons more energy, but experiments showed that kinetic energy depends on frequency, not intensity.

Particle nature of light

The Compton effect, where X-rays scatter off electrons with a wavelength shift, confirms that photons behave as particles with momentum.

Temperature and wavelength

Planck's law gives the spectral energy density as a function of wavelength (or frequency) and temperature, showing how radiation intensity varies with these parameters.

Electrons can be diffracted

The wave nature of electrons leads to observable phenomena like electron diffraction, which confirms the de Broglie hypothesis.

Increasing intensity

Classical Rayleigh-Jeans law predicted that intensity would increase without bound as wavelength decreases, leading to the ultraviolet catastrophe, which was resolved by Planck's quantization.

K_max = hν - φ

Einstein's photoelectric equation states that the maximum kinetic energy equals the photon energy minus the work function φ.

Davisson-Germer experiment

The Davisson-Germer experiment observed electron diffraction from a nickel crystal, confirming the wave nature of electrons.

Photons have momentum

The wavelength shift in Compton scattering can only be explained if photons carry momentum, supporting the particle nature of light.

Energy is emitted or absorbed in discrete quanta

Planck's theory introduced the idea that energy exchange between matter and radiation occurs in discrete packets or quanta.

Infinite energy at short wavelengths

The Rayleigh-Jeans law, based on classical equipartition, led to the ultraviolet catastrophe by predicting unbounded energy at short wavelengths.

Frequency

The stopping potential is directly proportional to the maximum kinetic energy of emitted electrons, which depends on the frequency of light, not its intensity.

Photoelectric effect

The photoelectric effect requires the particle nature of light; wave theory fails to explain why electron emission depends on frequency and not intensity.