Chapter 39: Problem 12
A beam of electrons is accelerated from rest through a potential difference of 0.100 kV and then passes through a thin slit. When viewed far from the slit, the diffracted beam shows its first diffraction minima at \(\pm\)14.6\(^\circ\) from the original direction of the beam. (a) Do we need to use relativity formulas? How do you know? (b) How wide is the slit?
Short Answer
Step by step solution
Determine Electron Speed
Evaluate Need for Relativity
Apply Diffraction Formula
Calculate Slit Width
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Kinetic Energy
- \( KE \) is the kinetic energy
- \( e \) is the elementary charge, approximately \( 1.6 \times 10^{-19} \, \text{C} \)
- \( V \) is the potential difference
de Broglie Wavelength
- \( \lambda \) is the de Broglie wavelength
- \( h \) is Planck's constant, \( 6.626 \times 10^{-34} \, \text{Js} \)
- \( m \) is the mass of the electron
- \( v \) is the speed of the electron obtained previously
Relativistic Mechanics
Diffraction Minimum
- \( a \) is the slit width
- \( \theta \) is the angle at which minimum occurs
- \( n \) is the order of the minimum, with 1 being the first minimum
- \( \lambda \) is the wavelength of electrons as per de Broglie's relation