Chapter 39: Problem 66
Coherent light is passed through two narrow slits whose separation is 20.0 \(\mu\)m. The second-order bright fringe in the interference pattern is located at an angle of 0.0300 rad. If electrons are used instead of light, what must the kinetic energy (in electron volts) of the electrons be if they are to produce an interference pattern for which the second-order maximum is also at 0.0300 rad?
Short Answer
Step by step solution
Understanding the Double Slit Experiment
Using the Interference Formula for Bright Fringes
Calculating the Wavelength for the Second-Order Maximum
Relating Electron Wavelength to Kinetic Energy
Solving for Electron Kinetic Energy
Final Answer
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Interference Patterns
Imagine a pond where two stones are dropped at once. The overlapping ripples create a similar pattern to that of the interference pattern seen through the slits. This is a hallmark of wave behavior and is evidence of wave-like properties in particles such as electrons.
de Broglie Wavelength
Electron Kinetic Energy
Constructive Interference
The formula for the condition of constructive interference is: \[ d \sin(\theta) = m\lambda \] where \( d \) is the distance between slits, \( \theta \) is the angle of observation, \( m \) is the order of the maximum (whole number), and \( \lambda \) is the wavelength. Recognizing the conditions for constructive interference helps predict where the bright spots form and aligns with understanding the underlying wave mechanics of particles. This ability to predict and confirm the existence of interference patterns through constructive interference is fundamentally significant in verifying wave-particle duality.