The Wave Particle Duality of Light

Flashcards covering the wave-particle duality of light, photon energy, the photoelectric effect, Compton scattering, and the Heisenberg uncertainty principle.

What four physical phenomena demonstrate that light behaves like a wave?

Reflection, refraction, diffraction, and interference.

What is meant by the wave-particle duality of light?

The concept that light exhibits both wave-like behaviors (such as interference and diffraction) and particle-like behaviors (such as the photoelectric effect and Compton scattering) depending on the situation.

How are photons defined in the particle model of light?

Photons are fundamental particles of light described as tiny packets or bundles of light energy.

What are the mass and electric charge of a photon?

A photon has zero mass and zero electric charge.

At what speed do photons travel in a vacuum?

In a vacuum, photons travel at the speed of light, $c = 3 \times 10^8\text{ m/s}$.

How are frequency ($f$) and wavelength ($\lambda$) related for a photon traveling at speed $c$?

They are indirectly proportional and related by the formula $f = \frac{c}{\lambda}$.

What is Planck's equation for calculating photon energy ($E$) using frequency ($f$)?

$E = h f$, where $h = 6.626 \times 10^{-34}\,J \cdot s$ is Planck's constant.

What is Planck's equation for calculating photon energy ($E$) using wavelength ($\lambda$)?

$E = \frac{h c}{\lambda}$, where $c = 3 \times 10^8\text{ m/s}$ is the speed of light.

How does photon energy change as frequency increases or wavelength decreases?

Higher frequency produces higher photon energy, and shorter wavelength produces higher photon energy.

What is the photoelectric effect?

The phenomenon where light shining on a metal surface ejects electrons (photoelectrons) instantly if the photon energy is sufficiently high.

What physical phenomenon is depicted in this diagram showing incident photons ejecting photoelectrons from a surface?

The photoelectric effect.

How is the threshold frequency ($f_0$) defined?

The minimum frequency of light required to eject electrons from a specific metal surface.

How is the work function ($W_0$) of a metal defined?

The minimum energy that an electron in a metal needs to be emitted from the metal surface.

What happens in the photoelectric effect if incident light has a frequency below the threshold frequency ($f_0$)?

No electrons are emitted, regardless of the light intensity.

What effect does increasing light intensity have when light frequency is above the threshold frequency ($f_0$)?

It increases the number of photoelectrons emitted.

Why did the photoelectric effect challenge classical wave theory?

Classical wave theory could not explain the existence of a threshold frequency or the immediate emission of photoelectrons.

What occurs during Compton scattering?

An X-ray or gamma-ray photon collides with an electron in an inelastic collision, transferring energy to the electron and scattering with a longer wavelength.

What collision process between a photon and an electron is illustrated in this diagram?

The Compton effect (or Compton scattering).

Why does a photon's wavelength increase after colliding with an electron in Compton scattering?

The photon loses energy to the electron, and since energy is inversely proportional to wavelength ($E = \frac{h c}{\lambda}$), losing energy increases the wavelength.

What does the Heisenberg Uncertainty Principle state?

It states that both the exact position and exact momentum of a quantum particle (such as an electron or photon) cannot be known simultaneously.

What is the formula for the Heisenberg Uncertainty Principle?

$\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$, where $\Delta x$ is position uncertainty, $\Delta p$ is momentum uncertainty, and $h$ is Planck's constant.

According to the Heisenberg Uncertainty Principle, how does reducing position uncertainty ($\Delta x$) affect momentum uncertainty ($\Delta p$)?

Making position more certain (smaller $\Delta x$) increases momentum uncertainty (larger $\Delta p$).

What is the energy of a photon with a wavelength of $500\text{ nm}$?

$E = 3.98 \times 10^{-19}\,J$, calculated using $E = \frac{h c}{\lambda}$ with $h = 6.626 \times 10^{-34}\,J \cdot s$, $c = 3.0 \times 10^8\text{ m/s}$, and $\lambda = 500 \times 10^{-9}\text{ m}$.

An electron is confined to a region of space with $\Delta x = 1.0 \times 10^{-10}\text{ m}$. What is the minimum uncertainty in its momentum ($\Delta p$)?

$\Delta p \ge 5.27 \times 10^{-25}\,kg \cdot m/s$, solved using $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$.