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Questions and Answers
What unique feature of Fery's black body allows it to behave as a perfect absorber?
Which part of Lummer and Pringsheim's experimental setup was crucial for dispersing radiation into a spectrum?
How was the temperature of the black body determined during the experiments conducted by Lummer and Pringsheim?
What is black body radiation primarily characterized by?
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What is the function of the inward conical projection in Fery's black body design?
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What is the correct expression for the de-Broglie wavelength associated with an electron in the non-relativistic case?
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Which of the following statements accurately differentiates between matter waves and electromagnetic (EM) waves?
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What is the fundamental equation derived by Schrödinger that describes the motion of a particle?
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What does the notation |Ψ|² represent in the Born interpretation of wavefunction?
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Which constant values need to be substituted to find the de-Broglie wavelength of an electron, according to the provided formulas?
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Study Notes
Blackbody
- A theoretical object absorbing all electromagnetic radiation incident on it.
- Also a perfect radiator of all wavelengths.
- A perfect blackbody does not exist in nature.
- Fery's blackbody consists of a double-walled hollow copper sphere, with a lamp black coating on the inside and nickel polish on the outside.
Blackbody Radiation Spectrum
- Lummer and Pringsheim conducted experiments on the energy distribution in the spectrum of blackbody radiation.
- The radiation was dispersed into a spectrum using a prism.
- The spectrum was focused onto a bolometer to measure the intensity of each line.
- The experiments were repeated at different temperatures.
De Broglie Wavelength of an Electron
- The wavelength of de Broglie waves associated with an electron is given by λ = h/√2meV, where:
- λ = wavelength
- h = Planck's constant
- m = electron mass
- e = electron charge
- V = accelerating voltage
Properties of Matter Waves
- Matter waves are associated with moving material particles.
- Particle and wave nature never appear simultaneously.
- Matter waves travel with the speed of the particle.
- They are generated from charged and neutral particles.
Difference between Matter Waves & EM Waves
- Electromagnetic waves travel at the speed of light, while matter waves travel at less than the speed of light.
- Electromagnetic waves do not need a medium, while matter waves require a medium.
- Electromagnetic waves are generated by charged particles, while matter waves are generated by both charged and neutral particles.
Wave Function
- The quantity whose variation builds up matter waves is called the wave function (Ψ).
- The value of the wave function at a particular point in space and time describes the probability of finding a particle at that point.
Born Interpretation of Wavefunction
- The absolute square of the wave function, |Ψ|^2, is called the probability density.
- The probability of finding the particle at a given point is proportional to |Ψ|^2 at that point.
- The integral of |Ψ|^2 over all space must equal 1, implying that the particle must be located somewhere in space.
Acceptable Wave Function
- Must be single-valued: A wave function cannot have multiple values at the same point.
- Must be finite everywhere: An infinite value would imply an infinitely large probability of finding the particle at that point.
- Must be continuous throughout space with a continuous first derivative.
Schrödinger Time-Independent Wave Equation
- A second-order differential equation for the wave function of a particle in a potential that does not vary with time.
- The equation is: ∂^2Ψ/∂x^2 + 2m(E-V)/h^2 Ψ = 0.
- Ψ = wave function
- m = mass of the particle
- E = total energy
- V = potential energy
- h = Planck's constant
Compton Effect
- The scattering of X-rays by electrons, resulting in an increase in the wavelength of the scattered X-ray.
- The shift in wavelength, Δλ, is given by Δλ = h/(moc)(1-cosΘ):
- Δλ = Compton shift
- h = Planck's constant
- m = electron mass
- o = speed of light
- Θ = scattering angle
Unmodified and Modified Radiation
- Unmodified Radiation: The scattered radiation with unchanged frequency.
- Modified Radiation: The scattered radiation with changed frequency.
Kinetic Energy of Recoiled Electron
- K.E. of the recoiled electron = hv - hν(✓(1+2asin^2(θ/2))/ (1+2asin^2(θ/2)) = hv - ( 2asin^2(θ/2)/(1+2asin^2(θ/z))
- hv = energy of incident photon
- hν' = energy of scattered photon
- a = hv/(moc^2)
- θ = scattering angle
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Description
Explore the fascinating concepts of blackbody radiation and de Broglie wavelengths. This quiz covers the characteristics of blackbodies, their relationship with temperature and experimental findings, as well as the properties of matter waves. Ideal for students delving into modern physics.
