An electron passes through a slit of width 1.0 ×10^-8 m. What is the uncertainty in the electro

step 1 In this exercise, we have an electron that passes through a slit that has a width of 10 to the m

An electron passes through a slit of width 1.0 ×10^-8 m....

An electron passes through a slit of width $1.0 \times 10^{-8} \mathrm{~m}$. What is the uncertainty in the electron's momentum component in the direction perpendicular to the slit but in the plane containing the slit?

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Key Concepts

Wave-Particle Duality

Wave-particle duality is the concept that quantum objects such as electrons exhibit both wave-like and particle-like properties. This dual nature is critical in understanding phenomena like diffraction patterns, as the electron's behavior when passing through a slit illustrates how confinement of its wave aspect leads to observable momentum uncertainty.

Heisenberg Uncertainty Principle

This fundamental principle of quantum mechanics establishes that certain pairs of physical properties, such as position and momentum, cannot both be precisely determined simultaneously. When an electron passes through a narrow slit, its position becomes confined, which increases the uncertainty in its momentum, particularly in the direction perpendicular to the slit.

Quantum Diffraction

When particles like electrons are constrained by a narrow slit, they display wave-like behavior by spreading out, or diffracting, after passing through. This diffraction is a manifestation of the inherent uncertainty in momentum resulting from the confinement of the electron's position, linking directly with the uncertainty principle.

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