Engineering Physics: Modern Physics

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Questions and Answers

What is the effective mass of a photon when it moves?

  • m = hv/c² (correct)
  • m = ℎν/c²
  • m = hv/c
  • m = h/λ

What is the momentum of a photon?

  • p = hv
  • p = ℎν/c²
  • p = hv/c (correct)
  • p = ℎ/λ

What is De-Broglie's hypothesis?

  • A moving particle of mass m and velocity v is not associated with a wave.
  • A moving particle of mass m and velocity v is associated with a photon.
  • A moving particle of mass m and velocity v is associated with a electromagnetic wave.
  • A moving particle of mass m and velocity v is associated with a wave. (correct)

What is the wavelength of matter wave associated with a particle of mass m and velocity v?

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

What is the expression for De-Broglie's wavelength of an electron accelerated by potential V?

<p>λ = 12.27/√V (D)</p> Signup and view all the answers

What is the property of matter waves in terms of velocity?

<p>The velocity of matter waves depends on the velocity of the particle. (B)</p> Signup and view all the answers

What is the Compton Effect?

<p>The phenomenon of the splitting of incident wavelength of x-rays into two components. (C)</p> Signup and view all the answers

What is the difference between the wavelength of the modified and unmodified radiations in Compton Effect?

<p>Δλ = λ` - λ (D)</p> Signup and view all the answers

What is the characteristic of matter waves?

<p>The wavelength of matter waves is inversely proportional to the mass of the particle. (B)</p> Signup and view all the answers

What is the expression for the kinetic energy of a particle?

<p>E = p²/2m (B)</p> Signup and view all the answers

What is the purpose of slits S1, S2, and S3 in the experimental setup of Compton Effect?

<p>To collimate the monochromatic beam of X-rays (D)</p> Signup and view all the answers

What was the limitation of the classical theory of light?

<p>All of the above (D)</p> Signup and view all the answers

What is the function of the crystal analyser in the experimental setup of Compton Effect?

<p>To reflect the scattered beam and disperse it into component wavelengths (C)</p> Signup and view all the answers

What is the significance of θ = 0° in the Compton scattering experiment?

<p>The Compton shift is zero (B)</p> Signup and view all the answers

What is the significance of Planck's photon hypothesis?

<p>It formed the basis of quantum theory (D)</p> Signup and view all the answers

What is the relationship between the Compton shift and the scattering angle?

<p>The Compton shift increases with an increase in scattering angle (A)</p> Signup and view all the answers

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

<p>The energy of a photon is directly proportional to its frequency (D)</p> Signup and view all the answers

What is the assumption made about the electrons in the scattering material in the derivation of the Compton shift?

<p>The electrons are at rest before collision with the photon (B)</p> Signup and view all the answers

What is the quantum of energy associated with a photon?

<p>hѵ (A)</p> Signup and view all the answers

What happens to the energy of a photon when it encounters matter?

<p>It is absorbed completely and vanishes (C)</p> Signup and view all the answers

What is the function of the ionization chamber in the experimental setup of Compton Effect?

<p>To measure the intensity of the reflected rays (D)</p> Signup and view all the answers

What is the nature of light energy according to Planck's hypothesis?

<p>It is discrete and concentrated in quanta (A)</p> Signup and view all the answers

What is the energy of the photon before collision with the electron?

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

What is the significance of the integer n in the equation E = nhѵ?

<p>It is an integer that determines the energy of the photon (D)</p> Signup and view all the answers

What is the name of the electron that gains energy and recoils with velocity v?

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

What is the velocity of a photon?

<p>c (A)</p> Signup and view all the answers

What is the purpose of rotating the ionization chamber along a circular scale?

<p>To detect X-rays of different wavelengths (D)</p> Signup and view all the answers

What is the nature of the scattering process involved in Compton Effect?

<p>Elastic collision (A)</p> Signup and view all the answers

What is the name of the phenomenon studied in this text?

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

What is the symbol for the rest mass of an electron?

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

What is the law applied to the X-component of momentum?

<p>Law of conservation of momentum (A)</p> Signup and view all the answers

What is the expression for relativistic mass?

<p>m = mo / sqrt(1 - v^2 / c^2) (B)</p> Signup and view all the answers

What is the symbol for the velocity of light?

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

What is the expression for Compton shift?

<p>∆λ = h / (2 * mo * c * (1 - cosθ)) (B)</p> Signup and view all the answers

What is the unit of Compton wavelength?

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

What is the value of ∆λ when θ = π/2?

<p>h / (2 * mo * c) (D)</p> Signup and view all the answers

What is the physical phenomenon studied in the equation mc^2 = h(ν - ν') + mo*c^2?

<p>Photon-electron collision (D)</p> Signup and view all the answers

What is the term for the quantity h / (mo * c)?

<p>Compton wavelength (A)</p> Signup and view all the answers

What is the greatest Compton shift due to a free electron?

<p>0.04852A0 (A)</p> Signup and view all the answers

Why are unmodified lines present in scattered radiation?

<p>Due to the interaction of photons with tightly bound electrons (D)</p> Signup and view all the answers

Why is the Compton shift not observed in heavy elements?

<p>Due to the small ratio of free electrons to tightly bound electrons (D)</p> Signup and view all the answers

What is the principle that states that the product of the uncertainty in determining position and momentum is greater than or equal to a constant?

<p>Heisenberg's Uncertainty Principle (C)</p> Signup and view all the answers

What is the expression for the de Broglie wavelength of a particle?

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

What is the condition for observing the Compton shift?

<p>θ = 180 degrees (B)</p> Signup and view all the answers

What is the relation between the wavelength and momentum of a particle according to de Broglie's hypothesis?

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

Why do some photons in the beam interact with free or valence electrons?

<p>Due to the high energy of the photons (B)</p> Signup and view all the answers

What is the expression for the Compton shift?

<p>Δλ = 2h/m0c sin²(θ/2) (B)</p> Signup and view all the answers

What is the condition for Heisenberg's Uncertainty Principle?

<p>Δx * Δp &gt;= h/2π (D)</p> Signup and view all the answers

What is the expression for the uncertainty in position of a particle in a wave packet?

<p>$Δx = 2π/Δk$ (A)</p> Signup and view all the answers

What is the relationship between the uncertainty in position and momentum of a particle?

<p>Δx.Δp = ℎ/2π (B)</p> Signup and view all the answers

What is the time-energy uncertainty principle?

<p>ΔE.Δt = ℎ/2π (B)</p> Signup and view all the answers

Why can't an electron exist inside the nucleus of an atom?

<p>Because the electron's energy would be too high (D)</p> Signup and view all the answers

What is the concept of binding energy of an electron in an atom based on the uncertainty principle?

<p>The energy required to free an electron from the nucleus (B)</p> Signup and view all the answers

What is the uncertainty in momentum of an electron in an atomic orbit?

<p>Δp ≥ ℎ/2πΔx (D)</p> Signup and view all the answers

What is the wavelength of a wave packet?

<p>λ = 2π/Δk (A)</p> Signup and view all the answers

What is the expression for the kinetic energy of a particle in terms of its momentum?

<p>E = p^2/2m (D)</p> Signup and view all the answers

What is the relationship between the uncertainty in position and momentum of a wave packet?

<p>Δx.Δp = ℎ/2π (C)</p> Signup and view all the answers

What is the implication of the uncertainty principle in measuring the energy of a particle?

<p>The energy of the particle cannot be precisely measured (B)</p> Signup and view all the answers

What is the expression for the kinetic energy of an electron in its orbit?

<p>ℎ² / 32𝜋²𝑅²𝑚 (B)</p> Signup and view all the answers

What is the significance of the wave function in quantum mechanics?

<p>It represents the probability density of finding a particle at a particular point. (A)</p> Signup and view all the answers

What is the condition for a wave function to be normalised?

<p>∫|ψ(x)|² dx = 1 (C)</p> Signup and view all the answers

What is the expression for the total energy of an electron in its orbit?

<p>ℎ² / 32𝜋²𝑅²𝑚 - 𝑍𝑒² / 4𝜋𝜀₀𝑅 (B)</p> Signup and view all the answers

What is the uncertainty principle in quantum mechanics?

<p>∆𝑥.∆𝑝𝑥 ≈ 2𝜋 (D)</p> Signup and view all the answers

What is the significance of the Compton effect?

<p>It demonstrates the particle nature of light. (B)</p> Signup and view all the answers

What is the expression for the energy of a recoiled electron in the Compton effect?

<p>ℎ - ℎ' (B)</p> Signup and view all the answers

What is the requirement for a wave function to be acceptable?

<p>It must be finite everywhere. (A)</p> Signup and view all the answers

What is the significance of the normalisation of a wave function?

<p>It ensures that the probability of finding a particle is always one. (B)</p> Signup and view all the answers

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

<p>E = ℎ𝜈 (A)</p> Signup and view all the answers

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Study Notes

  • Engineering Physics: Modern Physics*

Planck's Hypothesis

  • Planck's hypothesis states that energy is emitted or absorbed discontinuously in the form of photons or quanta.
  • Energy (E) is proportional to frequency (ν) of radiation, given by: E = hν, where h is Planck's constant.

Properties of Photons

  • Photons are individual packets of energy.
  • Photons have zero rest mass and cannot be accelerated.
  • Photons travel with speed of light (c) in vacuum.
  • Photon energy is proportional to its frequency.

De-Broglie's Hypothesis

  • De-Broglie's hypothesis states that a moving particle of mass m and velocity v is associated with a wave, known as a matter wave or de-Broglie wave.
  • Wavelength of matter wave (λ) is given by: λ = h / mv.

Properties of Matter Waves

  • Matter waves are generated by the motion of particles.
  • Wave nature of matter introduces uncertainty in position and momentum of particles.
  • Representation of matter waves is only symbolic.

Compton Effect

  • Compton effect is the phenomenon of splitting of incident X-ray wavelength into two components, with one wavelength shifted towards longer wavelengths.
  • Expression for Compton shift (Δλ) is given by: Δλ = (h/m0c)(1 - cosθ).

Heisenberg's Uncertainty Principle

  • Heisenberg's Uncertainty Principle states that the product of uncertainty in position (Δx) and momentum (Δp) of a particle### Electron Energy and Velocity
  • The mass of an electron is approximately 9.1 * 10^(-31) kg
  • If an electron exists inside the nucleus, its energy would be around 10 MeV
  • However, electrons emitted during β-decay have energies of only 3-4 MeV, so electrons cannot exist inside the nucleus

Binding Energy of an Electron in Atom

  • The concept of binding energy is based on the Uncertainty Principle
  • In an atom, an electron's position uncertainty (∆x) is approximately equal to the diameter of its orbit (2R)
  • The corresponding momentum uncertainty (∆px) is given by the equation: ∆px ≥ ℎ / (2π∆x)
  • The kinetic energy of an electron is given by the equation: K = ℎ² / (32π²R²m)
  • The potential energy of an electron in the field of a nucleus with atomic number Z is given by: V = -Ze² / (4πε₀R)
  • The total energy of an electron in its orbit is: E = K + V
  • The binding energy of an electron in an atom is approximately given by the equation: E = (ℎ² / (32π²R²m)) - (Ze² / (4πε₀R))

Wave Function and its Significance

  • A wave function is a mathematical function that describes the quantum state of a system
  • The square of the magnitude of the wave function (|ψ(x)|²) represents the probability density of finding a particle at a particular point
  • The wave function must be normalizable, finite everywhere, single-valued, continuous, and have a continuous first derivative everywhere
  • The wave function plays a crucial role in understanding quantum mechanics and is used to calculate probabilities and expectation values

Formulae

  • De-Broglie's Wavelength: λ = h / √(2mE)
  • Compton Effect: ∆λ = λ' - λ = h(1 - cosθ) / (m₀c)
  • Energy of recoiled electron: E = hν - hν'
  • Kinetic energy of recoiled electron: E = (1/2)mv²
  • Uncertainty Principle: ∆x∆px ≈ 2πℎ, ∆E∆t ≈ ℎ / (2π)

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