Physics Chapter: Wave-Particle Duality and Photoelectric Effect

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Questions and Answers

What does the variable 'N' represent in the equation q = Ne?

Number of photons

Number of elementary charges (correct)

Number of waves

Number of atoms

Which of the following correctly describes the nature of waves emitted by a blackbody?

No dependence on temperature

Only low-frequency waves are emitted

Continuous energy distribution

Quantized energy distribution (correct)

Why did Max Planck create a function of temperature?

To eliminate the UV catastrophe (correct)

To unify wave and particle theories

To match observed blackbody radiation spectra (correct)

To explain classical mechanics

What is the primary unit used to measure high energies in particle physics?

Electron volts Signup and view all the answers

At high frequencies and low wavelengths, what happens to the probability of an atom vibrating at that energy level?

It decreases Signup and view all the answers

In the context of kinetic energy, what does ΔE_k represent?

Change in kinetic energy Signup and view all the answers

What is the correct formula for the relativistic energy of a particle?

$E_T = E_{kr} + E_{rest}$ Signup and view all the answers

What does Planck's constant (h) quantify in terms of blackbody radiation?

The relationship between energy and frequency Signup and view all the answers

What happens to the energy of a photon when it collides with an X-ray of higher energy?

The energy of the photon decreases. Signup and view all the answers

How is the momentum of a photon calculated?

Using the formula $P = rac{E}{c}$. Signup and view all the answers

What effect does increasing the frequency of a photon have on its momentum?

It increases the momentum. Signup and view all the answers

What concept illustrates that light has both wave and particle properties?

Interference pattern created by electrons. Signup and view all the answers

Which formula relates the wavelength of a particle to its momentum?

$ heta = rac{h}{p}$. Signup and view all the answers

What is the consequence of having a small wavelength when measuring interference patterns?

The interference pattern becomes more pronounced. Signup and view all the answers

What condition is necessary for observing the wave nature of particles in the double-slit experiment?

The slit width must be smaller than the wavelength. Signup and view all the answers

In wave-particle duality, how does the wavelength of an electron compare to that of visible light?

The electron's wavelength is smaller than that of visible light. Signup and view all the answers

What does the photoelectric effect demonstrate about light?

Light has quantized energy that can eject electrons. Signup and view all the answers

What is the work function in the context of the photoelectric effect?

The minimum energy needed to eject an electron from a metal. Signup and view all the answers

How does increasing the frequency of light affect a photon?

It increases the energy carried by the photon. Signup and view all the answers

Which phenomenon provides evidence for the wave properties of light?

Double slit interference. Signup and view all the answers

What happens when light of a frequency lower than the threshold frequency strikes a metal?

No electrons are ejected, regardless of intensity. Signup and view all the answers

What is one of the characteristics of a photon?

It carries energy in discrete packets. Signup and view all the answers

In the photoelectric effect, what is the significance of the maximum kinetic energy equation $E_k = hf - W$?

It calculates the excess energy after removing the work function. Signup and view all the answers

What is the result of increasing the intensity of red light in the photoelectric effect?

It will not result in any electron ejection if the frequency is too low. Signup and view all the answers

What formula represents the relationship between total energy, rest energy, and kinetic energy?

$E_{kr} = E_{total} - E_{rest}$ Signup and view all the answers

Which of the following equations correctly defines kinetic energy in special relativity?

$E_{kr} = mc^2 \left(\frac{1}{\sqrt{1- \frac{v^2}{c^2}}}-1\right)$ Signup and view all the answers

What does the term 'Proper Time' refer to?

Both B and C Signup and view all the answers

In the context of special relativity, what does the variable 'V' represent?

The relative speed of the object compared to the observer Signup and view all the answers

Which of the following is a correct transformation equation for time in special relativity?

$Δt_O = rac{Δt_P}{\sqrt{1- \frac{v^2}{c^2}}}$ Signup and view all the answers

What is the physical meaning of 'Δt_P'?

Proper time experienced by an observer moving with the object Signup and view all the answers

If an object is moving at high speed, which of the following correctly describes the relationship between the observer's time and the proper time?

$Δt_O > Δt_P$ Signup and view all the answers

What equation represents the relationship between original and proper time considering relative speed?

$Δt_O^2 (c^2 - v^2) = c^2 Δt_P^2$ Signup and view all the answers

What happens when λ is large in relation to Δx during interference patterns?

Particles are more likely to miss the slits, preventing interference patterns. Signup and view all the answers

In quantum mechanics, what is the effect of measuring a particle's position?

It disturbs the particle and alters the system's behavior. Signup and view all the answers

What does the Heisenberg Uncertainty Principle state about measurements in quantum mechanics?

There will always be a degree of uncertainty in simultaneous measurements of position and momentum. Signup and view all the answers

What is the relationship between Δx and Δp in diffraction phenomena?

A small Δx contributes to a small Δp, enhancing the interference patterns. Signup and view all the answers

Which statement accurately describes the concept of wave functions in quantum mechanics?

Wave functions can display interference patterns when considering particle behavior. Signup and view all the answers

How does the size of an opening in diffraction affect Δx?

A larger opening causes Δx to become smaller. Signup and view all the answers

What does the 'quantum' in quantum theory refer to?

The smallest discrete value of a physical measurement. Signup and view all the answers

What is likely to occur if measurements of an electron's position are attempted?

The attempt will introduce uncertainty and alter the electron's behavior. Signup and view all the answers

What happens to Δt_O as V approaches c?

ΔtO approaches ∞ Signup and view all the answers

How does Δt_O compare to Δt_P when V is significantly less than c?

They are equal Signup and view all the answers

What is indicated if V is greater than or equal to c?

ΔtO becomes undefined Signup and view all the answers

For an observer on Earth, how long does a song last on a spacecraft moving at 0.90c compared to the Earth-bound duration?

Approximately 6.88 minutes Signup and view all the answers

Using the length contraction formula, what is the measured length (L_P) of a spaceship that has a proper length (L_V) of 78 m moving at 0.85c?

148 m Signup and view all the answers

What is a key consequence of an object moving at relativistic speeds?

Its kinetic energy increases significantly Signup and view all the answers

What does the equation P_r = P_P / √(1 - v²/c²) represent?

Relativistic momentum Signup and view all the answers

How does the time dilation formula change as speed increases?

ΔtO exceeds ΔtP Signup and view all the answers

Study Notes

Planck's Math and Wave-Particle Duality

Probability demonstrates wave-like behavior
Quantized energy (E = nhf) shows particle-like behavior
Small things exhibit both wave and particle properties
Double-slit interference experiment demonstrates wave nature
Photoelectric effect demonstrates particle nature
Light energy, in discrete packets (photons), interacts with electrons

Photoelectric Effect

Electrons are ejected from a metal when light hits it
A specific energy (threshold frequency) is needed for ejection
Higher-intensity light means more photons hitting the metal, but doesn't increase electron energy
Higher-frequency light means higher-energy photons, increasing electron kinetic energy
Energy of photon (E = hf) is related to the frequency (f) of light

Work Function

Work function (W) is the minimum energy needed to remove an electron from a metal
The relationship between kinetic energy of emitted electron (Ek) and frequency (f) of light is Ek = hf - W
The threshold frequency (fo) is the minimum frequency of light needed to eject electrons

Particle and Wave Duality

Light can behave as both a wave and a particle
The "particle" of light is a photon
The photoelectric effect, and other experiments, show light has particle-like properties
Wave-particle duality is a fundamental concept in quantum mechanics

Quantum Theory

Quantum theory describes the discrete nature of certain physical properties at the smallest scales
There is a smallest possible measure (quanta)
There is a limit to continuous measurements

Uncertainty Principle

It is impossible to simultaneously know a particle's position and momentum with perfect accuracy
A particle's position and momentum are linked by the principle of uncertainty. A change or measurement on one component directly alters the other component
ΔxΔp ≥ h/4π

Special Relativity

Measurements of time and distance depend on the observer's motion (frame of reference)
Time dilation occurs when time runs slower for observers in motion relative to a stationary observer.
The relationship between the stationary time and moving time =Δt = (Δt0)/ √(1-(v2/c2)). Δt0 is time measured by stationary observer and V is the velocity

General Relativity

Gravity arises from the distortion of spacetime by mass and energy
The effects of gravity on time and space are significant, and it has implications in measuring time

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Description

Explore the intriguing concepts of wave-particle duality and the photoelectric effect in this quiz. Understand how light exhibits both wave-like and particle-like properties through various experiments. Test your comprehension of fundamental physics principles that describe the behavior of light and electrons.