Practice Questions

Evaluate the effect on the energy of individual photons in a monochromatic light beam if its intensity is doubled.

Define the work function of a metal.

If the intensity of monochromatic radiation incident on a photosensitive surface is doubled, analyze the resulting change in the stopping potential and the saturation current.

Two metals, Tungsten ($\phi_0 = 4.5 \text{ eV}$) and Caesium ($\phi_0 = 2.14 \text{ eV}$), are considered for use as a filament in a vacuum tube for thermionic emission. Justify which metal would require a higher temperature to achieve significant thermionic emission and explain why.

The threshold wavelength for photoelectric emission from a certain metal is $600 \text{ nm}$. Solve for the work function of the metal in electron volts (eV).

Calculate the momentum of a photon corresponding to red light with a wavelength of $650 \text{ nm}$.

Identify the particle that represents a quantum of electromagnetic radiation.

Define the term 'threshold frequency'.

Justify why the stopping potential in a photoelectric experiment is independent of the intensity of the incident radiation, based on the photon picture of light.

A scientist claims to have deflected a beam of photons using a strong uniform magnetic field. Critique this claim.

List the three primary physical processes that can cause electron emission from a metal surface.

Recall the de Broglie relation for the wavelength of a moving particle.

A student argues, 'The wave theory of light can still explain the photoelectric effect if we consider that electrons need time to accumulate enough energy from a continuous wave. The instantaneous emission is just an experimental limitation.' Critique this argument based on the established observations of the photoelectric effect.

Justify the statement: 'The wave nature of matter is universal, but its effects are only significant for sub-atomic particles.' Support your justification with a comparative calculation for an electron moving at $10^6 \text{ m/s}$ and a cricket ball of mass $150 \text{ g}$ moving at $30 \text{ m/s}$.

Analyze why the wave theory of light fails to explain the instantaneous nature of the photoelectric effect.

Explain two reasons why the classical wave theory of light failed to explain the photoelectric effect.

List any three properties of photons.

A photon of wavelength $\lambda$ is completely absorbed by a stationary electron. Formulate an expression for the momentum transferred to the electron. Justify why, despite having no rest mass, a photon possesses momentum.

Light of wavelength $450 \text{ nm}$ is incident on a metal surface with a work function of $2.20 \text{ eV}$. Calculate the stopping potential required to stop the emission of photoelectrons.

Explain the term 'stopping potential' in the context of the photoelectric effect.

Calculate the de Broglie wavelength of an electron that has been accelerated from rest through a potential difference of $100 \text{ V}$.

A laser emits monochromatic light of frequency $5.0 \times 10^{14} \text{ Hz}$ at a power of $3.0 \times 10^{-3} \text{ W}$. Calculate the number of photons emitted by the source per second.

Apply Einstein's photoelectric equation to determine if a silver surface, with a work function of $4.7 \text{ eV}$, will exhibit photoelectric emission when illuminated by ultraviolet light of wavelength $250 \text{ nm}$.

Examine the graphical representation of stopping potential ($V_0$) versus frequency ($\nu$) for photoelectric emission from two different metals, A and B. What physical quantities do the slope and the x-intercept of these graphs represent, and how do they compare for the two metals?

Demonstrate how Einstein's photoelectric equation, $K_{\text{max}} = h\nu - \phi_0$, logically leads to the concept of a threshold frequency.

In a photoelectric effect experiment, the stopping potential is measured to be $1.8 \text{ V}$. Solve for the maximum speed of the emitted photoelectrons.

Formulate the relationship between the threshold wavelength ($\lambda_0$) and the work function ($\phi_0$) of a metal. Using this, propose a reason why alkali metals are suitable for photoelectric experiments using visible light, while metals like zinc require ultraviolet light.

In a photoelectric effect experiment, the stopping potential ($V_0$) versus frequency ($\nu$) data for two different photosensitive materials, M1 and M2, are plotted. The work function of M1 is $\phi_1$ and M2 is $\phi_2$, with $\phi_1 > \phi_2$. Create a single graph showing the expected plots for both M1 and M2. Justify the key features of your graph, including the slopes and the x-intercepts (threshold frequencies).

Propose a simple conceptual design for a device that utilizes field emission. Explain the underlying principle and justify why a very strong electric field, typically of the order of $10^8 \text{ V/m}$, is necessary for this process.

Evaluate the statement: 'An experiment can simultaneously demonstrate both the wave and particle nature of light.' Justify your position with reference to phenomena like the photoelectric effect and Young's double-slit experiment.

Recall the formula for the energy of a photon and calculate it for a light of frequency $5.0 \times 10^{14} \text{ Hz}$. (Use Planck's constant $h = 6.63 \times 10^{-34} \text{ J s}$)

Describe how the photoelectric current and the stopping potential are affected when the intensity of incident radiation is increased, while its frequency is kept constant and above the threshold frequency.

Recall the de Broglie wavelength formula and calculate the wavelength for an electron having a momentum of $5.0 \times 10^{-24} \text{ kg m/s}$. (Use $h = 6.63 \times 10^{-34} \text{ J s}$)

Recall Einstein's photoelectric equation and explain each term in the equation.

Compare and contrast the effect of increasing the intensity versus increasing the frequency of incident radiation on the photoelectric effect, assuming the initial frequency is above the threshold frequency.

An electron, a proton, and an alpha particle are all accelerated through the same potential difference, $V$. Evaluate and compare their resulting de Broglie wavelengths. Propose a mathematical relationship to show which particle will have the longest wavelength and which will have the shortest.

Compare the de Broglie wavelengths of a $0.15 \text{ kg}$ cricket ball moving at $30 \text{ m/s}$ and an electron moving at the same speed. Analyze why the wave nature of the cricket ball is not observable.

Two different metals, Metal A (work function $\phi_A = 2.5 \text{ eV}$) and Metal B (work function $\phi_B = 4.5 \text{ eV}$), are illuminated by the same monochromatic light source of wavelength $400 \text{ nm}$. Evaluate which metal will emit photoelectrons with greater maximum kinetic energy. Justify your conclusion with detailed calculations.

An electron and a proton have the same de Broglie wavelength. Analyze which particle has a higher kinetic energy and by what factor.

Design an experiment to verify the relationship between the stopping potential ($V_0$) and the frequency ($\nu$) of incident radiation. Your design should include a labeled diagram of the setup, the procedure, and a justification for how the collected data would be used to determine Planck's constant ($h$) and the work function ($\phi_0$) of the emitter material.

Explain the concept of the dual nature of matter as proposed by Louis de Broglie. Why is this wave nature not apparent for macroscopic objects?

The work function of a metal is $2.0 \text{ eV}$. Recall the formula for threshold frequency and calculate its value. (Use $1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$ and $h = 6.63 \times 10^{-34} \text{ J s}$)

Examine the relationship between the de Broglie wavelength ($\lambda$) and the kinetic energy ($K$) of a non-relativistic particle. Demonstrate mathematically whether $\lambda$ is inversely proportional to $K$ or to $\sqrt{K}$.

Propose a method to control the de Broglie wavelength of an electron beam. Derive a formula that relates the de Broglie wavelength ($\lambda$) of an electron to the potential difference ($V$) used to accelerate it from rest. Evaluate the potential difference required to produce an electron beam with a de Broglie wavelength of $0.1 \text{ nm}$.

Summarize the key experimental observations of the photoelectric effect.