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?

λ = h/mv Signup and view all the answers

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

λ = 12.27/√V Signup and view all the answers

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

The velocity of matter waves depends on the velocity of the particle. Signup and view all the answers

What is the Compton Effect?

The phenomenon of the splitting of incident wavelength of x-rays into two components. Signup and view all the answers

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

Δλ = λ` - λ Signup and view all the answers

What is the characteristic of matter waves?

The wavelength of matter waves is inversely proportional to the mass of the particle. Signup and view all the answers

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

E = p²/2m Signup and view all the answers

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

To collimate the monochromatic beam of X-rays Signup and view all the answers

What was the limitation of the classical theory of light?

All of the above Signup and view all the answers

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

To reflect the scattered beam and disperse it into component wavelengths Signup and view all the answers

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

The Compton shift is zero Signup and view all the answers

What is the significance of Planck's photon hypothesis?

It formed the basis of quantum theory Signup and view all the answers

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

The Compton shift increases with an increase in scattering angle Signup and view all the answers

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

The energy of a photon is directly proportional to its frequency 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?

The electrons are at rest before collision with the photon Signup and view all the answers

What is the quantum of energy associated with a photon?

hѵ Signup and view all the answers

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

It is absorbed completely and vanishes Signup and view all the answers

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

To measure the intensity of the reflected rays Signup and view all the answers

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

It is discrete and concentrated in quanta Signup and view all the answers

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

hѵ Signup and view all the answers

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

It is an integer that determines the energy of the photon Signup and view all the answers

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

Recoil electron Signup and view all the answers

What is the velocity of a photon?

c Signup and view all the answers

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

To detect X-rays of different wavelengths Signup and view all the answers

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

Elastic collision Signup and view all the answers

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

Compton shift Signup and view all the answers

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

mo Signup and view all the answers

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

Law of conservation of momentum Signup and view all the answers

What is the expression for relativistic mass?

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

What is the symbol for the velocity of light?

c Signup and view all the answers

What is the expression for Compton shift?

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

What is the unit of Compton wavelength?

angstrom Signup and view all the answers

What is the value of ∆λ when θ = π/2?

h / (2 * mo * c) Signup and view all the answers

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

Photon-electron collision Signup and view all the answers

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

Compton wavelength Signup and view all the answers

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

0.04852A0 Signup and view all the answers

Why are unmodified lines present in scattered radiation?

Due to the interaction of photons with tightly bound electrons Signup and view all the answers

Why is the Compton shift not observed in heavy elements?

Due to the small ratio of free electrons to tightly bound electrons 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?

Heisenberg's Uncertainty Principle Signup and view all the answers

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

λ = h/p Signup and view all the answers

What is the condition for observing the Compton shift?

θ = 180 degrees Signup and view all the answers

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

λ = h/p Signup and view all the answers

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

Due to the high energy of the photons Signup and view all the answers

What is the expression for the Compton shift?

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

What is the condition for Heisenberg's Uncertainty Principle?

Δx * Δp >= h/2π Signup and view all the answers

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

$Δx = 2π/Δk$ Signup and view all the answers

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

Δx.Δp = ℎ/2π Signup and view all the answers

What is the time-energy uncertainty principle?

ΔE.Δt = ℎ/2π Signup and view all the answers

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

Because the electron's energy would be too high Signup and view all the answers

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

The energy required to free an electron from the nucleus Signup and view all the answers

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

Δp ≥ ℎ/2πΔx Signup and view all the answers

What is the wavelength of a wave packet?

λ = 2π/Δk Signup and view all the answers

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

E = p^2/2m Signup and view all the answers

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

Δx.Δp = ℎ/2π Signup and view all the answers

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

The energy of the particle cannot be precisely measured Signup and view all the answers

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

ℎ² / 32𝜋²𝑅²𝑚 Signup and view all the answers

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

It represents the probability density of finding a particle at a particular point. Signup and view all the answers

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

∫|ψ(x)|² dx = 1 Signup and view all the answers

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

ℎ² / 32𝜋²𝑅²𝑚 - 𝑍𝑒² / 4𝜋𝜀₀𝑅 Signup and view all the answers

What is the uncertainty principle in quantum mechanics?

∆𝑥.∆𝑝𝑥 ≈ 2𝜋 Signup and view all the answers

What is the significance of the Compton effect?

It demonstrates the particle nature of light. Signup and view all the answers

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

ℎ - ℎ' Signup and view all the answers

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

It must be finite everywhere. Signup and view all the answers

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

It ensures that the probability of finding a particle is always one. Signup and view all the answers

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

E = ℎ𝜈 Signup and view all the answers

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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Description

This quiz covers modern physics topics including Planck's hypothesis, properties of photons, de-Broglie hypothesis, and wave-particle duality.