Einstein won the Nobel Prize in physics for the photo-electric effect in 1924 for hisinterpretation of the photoelectric effect in a paper published in 1905 when he was 26years old. This work resulted in the Einstein-Planck Equation for the energy of a photon:E = hv = (h/2n) 0Similarly, Louis de Broglie, in his 1924 Ph.D. thesis proposed that just as light (and otherelectromagnetic waves) has both wave-like and particle-like properties, matter (and inparticular electrons) has wave-like properties and that the momentum p of these matterwaves have a momentum given by:p= h/2 = (h/2z)k, where, as in class, k = 2wnIn both equations, h is Planck's constant = 6.62607004 x 1034 m²kg/sa) using Ao At = 1, show that AE At = (h/2n)b) using Az Ak = 1, show that Az Ap = (h/2R)c) Since momentum p = mass times velocity = mv, use another of Einstein's favoriteequations, E = mc? to write p = E/c for a photon or electron, and using the Einstein-PlanckEquation obtain de Broglie's formula for momentum.

a) As per Einstein-Planck’s equation, photon’s energy can be represented as, Here, h, ν, and ω…

a) using Ao At = 1, show that AE At = (h/2x) b) using Az Ak = 1, show that Az Ap = (h/2r) c) Since momentum p = mass times velocity = mv, use another of Einstein's favorite equations, E = mc² to write p = E/cfor a photon or electron, and using the Einstein-Planck Equation obtain de Broglie's formula for momentum.

a) using Ao At = 1, show that AE At = (h/2x) b) using Az Ak = 1, show that Az Ap = (h/2r) c) Since momentum p = mass times velocity = mv, use another of Einstein's favorite equations, E = mc² to write p = E/cfor a photon or electron, and using the Einstein-Planck Equation obtain de Broglie's formula for momentum.

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter27: Quantum Theory

Section: Chapter Questions

Problem 3STP

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Concept explainers

Wien's displacement law

Students often get confused between Wien's displacement law and Planck's radiation law. Although both are historically related, yet they are conceptually different. Planck's law helps determine the spectrum of a blackbody, while Wien's law determines the relationship between peak wavelength and temperature.

Question

Einstein won the Nobel Prize in physics for the photo-electric effect in 1924 for his
interpretation of the photoelectric effect in a paper published in 1905 when he was 26
years old. This work resulted in the Einstein-Planck Equation for the energy of a photon:
E = hv = (h/2n) 0
Similarly, Louis de Broglie, in his 1924 Ph.D. thesis proposed that just as light (and other
electromagnetic waves) has both wave-like and particle-like properties, matter (and in
particular electrons) has wave-like properties and that the momentum p of these matter
waves have a momentum given by:
p= h/2 = (h/2z)k, where, as in class, k = 2wn
In both equations, h is Planck's constant = 6.62607004 x 1034 m²kg/s
a) using Ao At = 1, show that AE At = (h/2n)
b) using Az Ak = 1, show that Az Ap = (h/2R)
c) Since momentum p = mass times velocity = mv, use another of Einstein's favorite
equations, E = mc? to write p = E/c for a photon or electron, and using the Einstein-Planck
Equation obtain de Broglie's formula for momentum.

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