Sketch the interference pattern that results from the diffraction of electrons passing through two closely spaced slits.

Verified step by step guidance

1. Understand that the problem involves electron diffraction, which is a quantum mechanical phenomenon where electrons exhibit wave-like behavior.
2. Recall that the interference pattern is similar to that of light passing through a double slit, resulting in alternating bright and dark fringes due to constructive and destructive interference.
3. Identify that the spacing between the slits and the wavelength of the electrons will affect the pattern. The electron wavelength can be determined using the de Broglie wavelength formula: \( \lambda = \frac{h}{mv} \), where \( h \) is Planck's constant, \( m \) is the mass of the electron, and \( v \) is its velocity.
4. Sketch the pattern by drawing a series of parallel lines on a screen, with the central maximum being the brightest and the intensity of the fringes decreasing as you move away from the center.
5. Label the central maximum and note that the distance between the fringes is related to the wavelength and the slit separation, which can be calculated using the formula for double-slit interference: \( d \sin \theta = m \lambda \), where \( d \) is the slit separation, \( \theta \) is the angle of the fringe, \( m \) is the order of the fringe, and \( \lambda \) is the wavelength.

Key Concepts

Wave-Particle Duality

Wave-particle duality is a fundamental concept in quantum mechanics that describes how particles, such as electrons, exhibit both wave-like and particle-like properties. When electrons pass through slits, they can interfere with themselves as waves, leading to patterns that are characteristic of wave behavior, such as constructive and destructive interference.

Diffraction

Diffraction is the bending of waves around obstacles and the spreading of waves when they pass through narrow openings. In the context of electrons passing through slits, diffraction occurs as the electron waves spread out after passing through the slits, creating an interference pattern on a detection screen, which is a hallmark of wave behavior.

Interference Pattern

An interference pattern is a pattern formed by the overlapping of two or more waves, resulting in regions of constructive interference (bright spots) and destructive interference (dark spots). In the case of electrons passing through two slits, the resulting pattern on a screen demonstrates the wave nature of electrons, with alternating bright and dark fringes that reflect the probability distribution of where electrons are likely to be detected.