Modern Physics-I: Photoelectric Effect
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Questions and Answers

What is the energy of a photon with a wavelength of 4000 Å expressed in joules?

  • $2.5 \times 10^{-19}$ J
  • $3.2 \times 10^{-19}$ J
  • $5.5 \times 10^{-19}$ J
  • $4.96 \times 10^{-19}$ J (correct)

How many photons are emitted by a 60 milliwatt bulb with a wavelength of light measuring 6000 Å?

  • $2.4 \times 10^{17}$ photon/sec
  • $1.1 \times 10^{17}$ photon/sec
  • $3.5 \times 10^{17}$ photon/sec
  • $1.8 \times 10^{17}$ photon/sec (correct)

What is the average energy of a photon with a wavelength of 550 nm?

  • $1.89 \times 10^{-19}$ J
  • $3.616 \times 10^{-19}$ J (correct)
  • $2.26 \times 10^{-19}$ J
  • $4.15 \times 10^{-19}$ J

If the energy flux of sunlight is 1.388 × 10^3 W/m², how many photons strike one square meter per second, assuming each photon has a wavelength of 550 nm?

<p>$3.83 \times 10^{21}$ photon/m²s (D)</p> Signup and view all the answers

To exert a force of 1N on a totally reflecting screen, how many photons with a wavelength of 6600 nm must strike it per second?

<p>2.42 × 10^{20} photons/s (C)</p> Signup and view all the answers

What is the relationship between the energy of a photon and its frequency?

<p>E is directly proportional to ν (C)</p> Signup and view all the answers

What does the equation E = hc/λ express?

<p>The energy of a photon as a function of its wavelength. (C)</p> Signup and view all the answers

Which of the following correctly states the effective mass of a photon?

<p>It is dependent on its wavelength. (D)</p> Signup and view all the answers

In the context of photon momentum, which equation is correct?

<p>p = h/λ (D)</p> Signup and view all the answers

How is the intensity of light defined in terms of energy and area?

<p>I = N(hν)/A (D)</p> Signup and view all the answers

What is the rest mass of a photon?

<p>Zero (C)</p> Signup and view all the answers

Which statement about the relationship between color and the effective mass of photons is accurate?

<p>Violet light photons have greater effective mass than red light photons. (A)</p> Signup and view all the answers

What unit is used to measure the intensity of light, based on the definition involving power?

<p>Watt per square meter (C)</p> Signup and view all the answers

What happens to the photo current when the positive potential of A is gradually increased?

<p>It increases until it reaches a maximum known as saturation current. (D)</p> Signup and view all the answers

What is defined as the stopping potential (V0)?

<p>The maximum negative potential at which the photo current becomes zero. (B)</p> Signup and view all the answers

How does an increase in light intensity affect the stopping potential (V0)?

<p>It increases photo current while keeping V0 unchanged. (D)</p> Signup and view all the answers

What is the relationship between the maximum kinetic energy of photo electrons and the stopping potential?

<p>Kmax is calculated by $Kmax = eV0$. (D)</p> Signup and view all the answers

Which of the following statements is true about the photo emissive plate in relation to the potentials A and C?

<p>A remains positive with respect to C during the initial phase of photo current increase. (D)</p> Signup and view all the answers

What is the change in momentum for the incident photon after reflection?

<p>$\frac{h}{\lambda}$ (B)</p> Signup and view all the answers

If the wavelength of an incident photon is $500 \text{ nm}$, what is the corresponding energy of the photon?

<p>$3.76 \text{ eV}$ (B)</p> Signup and view all the answers

In a scenario where the power through a cross-section is $10 \text{ W}$ and the wavelength is $500 \text{ nm}$, how many photons are absorbed per second?

<p>$1.2 \times 10^{19}$ photons/s (B)</p> Signup and view all the answers

Which photon color possesses higher energy?

<p>Violet (B)</p> Signup and view all the answers

At a signal frequency of $10 \text{ MHz}$ and power of $100 \text{ MW}$ for a TV station, how many photons are radiated per second?

<p>$6.25 \times 10^{16}$ photons/s (A)</p> Signup and view all the answers

How many photons pass through a unit area per second if light of intensity $100 \text{ W/m}^2$ and wavelength $400 \text{ nm}$ is incident?

<p>$5.0 \times 10^{21}$ (B)</p> Signup and view all the answers

What is the efficiency-adjusted power output of a light bulb that converts 60 W of electrical energy into light energy with 50% efficiency?

<p>$30 \text{ W}$ (A)</p> Signup and view all the answers

During its lifetime of one day, how many photons does a light bulb emitting monochromatic light at $700 \text{ nm}$ and powered at $60 \text{ W}$ emit?

<p>$1.2 \times 10^{23}$ (B)</p> Signup and view all the answers

What does the equation 2πr = n÷lambda signify in the context of an electron's motion?

<p>The circumference of the electron's path corresponds to an integral multiple of its wavelength. (D)</p> Signup and view all the answers

How is the angle of diffraction, φ, related to the glancing angle, θ?

<p>φ = 180° - 2θ. (C)</p> Signup and view all the answers

What does the variable λ represent in the context of the Bohr model?

<p>The de Broglie wavelength associated with the electron. (D)</p> Signup and view all the answers

In the Bohr quantization condition, what physical quantity does 'n' denote?

<p>The quantum number corresponding to the electron's orbit. (B)</p> Signup and view all the answers

For an electron in the sixth Bohr orbit, which relation holds true regarding its de Broglie wavelength?

<p>It is an integer fraction of the orbit's circumference. (C)</p> Signup and view all the answers

Which of the following best describes the motion of an electron according to the Bohr model?

<p>Electrons move in stable orbits defined by quantized energy levels. (C)</p> Signup and view all the answers

What is represented by 'mvr = \frac{nh}{2\pi}' in the context of electron motion?

<p>The quantization of angular momentum for an electron in a stable orbit. (C)</p> Signup and view all the answers

What is the significance of stationary waves in the context of an electron's orbit?

<p>They imply that electrons can only exist in certain defined orbits. (D)</p> Signup and view all the answers

What happens to the wavelength of a particle if its momentum is defined precisely?

<p>The wavelength is definite and extends through all space. (A)</p> Signup and view all the answers

In the context of wave packets, what does the term 'superposition' refer to?

<p>Combining multiple waves with varying wavelengths. (A)</p> Signup and view all the answers

According to the uncertainty principle, what is the relationship between the uncertainties in position and momentum?

<p>Minimizing one uncertainty increases the other. (B)</p> Signup and view all the answers

What is the significance of the phase velocity of a matter wave?

<p>It has no physical significance. (B)</p> Signup and view all the answers

In the photoelectric effect, what denotes the energy absorption process?

<p>Absorption in discrete energy units. (A)</p> Signup and view all the answers

What is implied by the stopping potential in the context of the photoelectric effect?

<p>It varies with frequency and is not affected by intensity. (A)</p> Signup and view all the answers

What is the primary implication of a particle being confined to a finite region?

<p>It possesses multiple wavelengths. (A)</p> Signup and view all the answers

What aspect of quantum wave theory is still under research?

<p>The dual nature of matter and detailed physical explanations. (B)</p> Signup and view all the answers

Flashcards

Photon Energy Formula

The energy (E) of a photon is directly proportional to its frequency (ν) and is given by E = hν. Where h is Planck's constant.

Photon Energy (Alternative)

Photon energy can also be expressed as E = hc/λ, where c is the speed of light and λ is the wavelength of the photon. hc is a constant.

Photon Linear Momentum

The linear momentum (p) of a photon is its energy (E) divided by the speed of light (c); p = E/c = hν/c = h/λ.

Photon Effective Mass

The effective mass (m) of a photon is its energy (E) divided by the speed of light squared (c²); m = E/c². Rest mass is zero.

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Photon Mass Relation to Wavelength

A photon's effective mass is inversely proportional to its wavelength, so shorter wavelengths lead to higher effective mass.

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Photon Intensity

Intensity (I) of light is power (P) per unit area (A); I = P/A. Energy incident per unit area per unit time.

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Intensity and Photon Number

Light intensity is also related to the number of photons (N) hitting an area (A) over a time (t) and each carrying energy (hν). I = N(hν) / (At)

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Planck's Constant

A fundamental constant in quantum mechanics (h = 6.626 × 10⁻³⁴ J·s) that relates a photon's energy to its frequency.

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Photon Energy Calculation

The energy of a photon is inversely proportional to its wavelength. It can be calculated using the equation E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength.

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Photon Flux

The rate at which photons are emitted from a source, usually measured as photons per second or photons per unit area per second.

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Energy Flux of Sunlight

The power per unit area of sunlight incident on a surface. It's commonly measured in watts per square meter (W/m²).

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Photon/second calculation

The number of photons emitted from a source per second can be calculated by dividing the power (in watts) of the source by the energy of a single photon.

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Force from photons

The force exerted by photons on a totally reflecting surface is related to the rate at which photons strike the surface. It depends on the number of photons per second and the momentum of the photons.

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What is the Photoelectric effect?

The emission of electrons from a metal when light falls on it. The emitted electrons are called photoelectrons.

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What is Stopping Potential?

The minimum negative potential applied to the anode (A) that stops all photoelectrons from reaching it.

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What does Stopping Potential measure?

Stopping potential (V0) measures the maximum kinetic energy (Kmax) of the photoelectrons.

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How does intensity affect the photoelectric effect?

Increasing the intensity of light increases the photocurrent (number of photoelectrons) but does not change the stopping potential.

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What is saturation current?

The maximum photocurrent that can be achieved by increasing the intensity of light.

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Photoelectric Effect

The emission of electrons from a metal surface when light shines on it.

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Photon Energy

The energy carried by a single photon, related to its frequency (ν) by E = hν, where h is Planck's constant.

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Photon Momentum

The momentum of a photon, calculated as p = h/λ, where h is Planck's constant and λ is the photon's wavelength.

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Force from Light

Light can exert a force on a surface by transferring momentum to it.

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Photon Absorption

When a photon is absorbed by a surface, its energy is transferred to the surface.

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Photon Energy and Color

Different colors of light have different energies. Violet light has the most energy, and red light has the least energy.

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Photon Emission

The process by which an atom or molecule releases a photon, losing energy in the process.

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De Broglie Wavelength

The wavelength associated with a moving particle, specifically an electron in this context, determined by its momentum.

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Bohr Quantisation Condition

The condition that dictates electrons can only occupy specific circular orbits around the nucleus, where the circumference of the orbit is an integral multiple of the electron's De Broglie wavelength.

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Electron as a Standing Wave

In Bohr's model, electrons orbiting the nucleus are described as standing waves, like a vibrating string fixed at both ends, with a specific, quantized wavelength.

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Why are electron orbits quantized?

Due to the wave nature of electrons, only certain wavelengths can lead to stable orbits, resulting in specific energy levels, or quantized orbits.

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Electron Orbit Circumference

The circumference of an electron's orbit must be a whole number multiple of its De Broglie wavelength for a stable orbit to exist.

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Quantized Electron Energy

The Bohr model postulates that electrons can only occupy certain energy levels determined by the quantization condition, resulting in specific energy values.

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What is the role of 'n'?

The integer 'n' in the Bohr quantization condition represents the principal quantum number, defining the specific energy level of an electron and the size of the orbit.

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Wavepacket

A wavepacket is a localized wave formed by the superposition of multiple waves with different wavelengths. It has a finite extent in space (∆x = finite) and a finite range of momenta (∆p = finite).

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Wave Function (ψ)

The wave function (ψ) in quantum mechanics describes the probability amplitude of a particle. The square of the wave function (|ψ|²) represents the probability of finding the particle in a specific volume.

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Uncertainty Principle

The Uncertainty Principle states that it is impossible to simultaneously determine both the position (∆x) and momentum (∆p) of a particle with absolute certainty. The product of the uncertainties in position and momentum must be greater than or equal to Planck's constant divided by 4π.

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Wave-particle Duality

Wave-particle duality is the concept that matter exhibits both wave-like and particle-like behaviors.

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Stopping Potential

The stopping potential is the minimum negative potential difference that needs to be applied to an electron-emitting material to stop the photoelectric current. It is independent of the intensity of the incident light and depends only on its frequency.

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Phase Velocity (vp)

Phase velocity refers to the speed at which a point of constant phase travels in a wave. For matter waves, the phase velocity has no physical significance.

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Study Notes

Modern Physics-I

  • Photoelectric Effect:

    • Ejection of electrons from a metal surface when light of a suitable frequency or wavelength shines on it.
    • Ejected electrons are called photoelectrons.
    • The current flowing due to photoelectrons is called photoelectric current.
    • Discovered by Hertz.
    • Laws of photoelectric effect were given by Lenard.
    • Explained by Einstein using Quantum theory of light
    • Different experiments, Hertz, Hallwach, Lenard - key experiments
    • Work function - minimum energy required for electron ejection
    • Types of electron emission: Thermionic, Field, Photoelectric
    • Quantum theory - Energy of photon, E = hv (where h = Planck's constant, v = frequency). E = hc/λ, (where c = speed of light, λ= wavelength).

  • Quantum Theory:

    • Energy radiated from a source propagates in the form of small packets called photons
    • Energy of a photon is directly proportional to the frequency of radiation (E = hv)
    • Energy of a photon is inversely proportional to its wavelength (E = hc/λ).
    • Rest mass of a photon is zero.

  • Intensity of Light:

    • Energy passing through per unit area per unit time.
    • I = Energy/Area/Time
    • Intensity of light is related to number of photons per second

  • Radiation force and Radiation pressure:

    • When radiation falls on a surface, force and pressure are exerted.
    • Force depends on the number of incident photons, wavelength, and nature of surface (reflecting/absorbing).

  • Linear momentum of photon: -p = E/c (where E is energy of the photon, c is the speed of light) = hv/c = h/λ -So mass of violet light photon is greater than the mass of red light photon. (λ<λv)

  • Effective mass of photon: -m = E/c² = hc/c²λ = h/cλ (where E is energy, c is speed of light)

  • Intensity of light related to number of photons per second:

    • I = n(hv)/A (where n is number of photons, h is Planck's constant, v is frequency, A is area)

  • Louis Victor de Broglie (1892-1987):

    • French physicist who proposed the wave nature of matter
    • Developed wave mechanics, a concept related to the wave-like behavior of matter
    • A key concept in quantum mechanics

  • Philipp Eduard Anton von Lenard (1862-1947):

    • German physicist who discovered many properties of cathode rays, winning a Nobel Prize

  • De-Broglie Hypothesis: -Matter can exhibit both particle and wave-like properties -Wavelength associated with a particle (de Broglie wavelength) = h/p (where h = Planck's constant and p = momentum)

  • de-Broglie Wavelength associated with moving particles and charged particles:

    • λ = h/√2mE if E=1/2mv^2, where, m = mass, v = velocity, h is Plank's constant, and E is Kinetic energy.
    • λ = h/mv Or λ = h/√2mqV (where q is charge) or λ = h/√2mKE (where KE is kinetic energy)

  • Davisson–Germer experiment:

    • Crucial experiment demonstrating the wave nature of electrons
    • Helped confirm De Broglie's hypothesis
    • Electrons diffracted by nickel crystals

  • Bohr Quantization condition:

    • Electron orbits are quantized, with circumference being an integer multiple of the de Broglie wavelength.
    • 2πr = nλ

  • Photo Cell:

    • Practical application of photoelectric effect
    • Converts light energy into electrical energy
    • Construction of photo cells
    • Applications of photo cells (television cameras, automatic doors)

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Explore the fundamentals of the photoelectric effect in this quiz. Learn about the ejection of electrons, key experiments, and the role of quantum theory in explaining this phenomenon. Test your understanding of concepts such as work function and types of electron emission.

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