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The diffraction phenomenon can be observed whenever the wavelength is comparable in magnitude to...

Question:

The diffraction phenomenon can be observed whenever the wavelength is comparable in magnitude to the size of the slit opening. To be "diffracted", how fast must a person weighing 84 kg move through a door that is 1 m wide?

Velocity:

In physics, the term velocity is most widely used, and it can be defined as changing the position of the particle with respect to the time. The measurable standard unit of the velocity is meter per second.

Answer and Explanation:

The mass of the person is {eq}m = 84\,{\rm{kg}} {/eq}

  • The wide is {eq}\lambda = 1\,{\rm{m}} {/eq}


The expression for the de-Broglie wavelength is given by

{eq}\begin{align*} \lambda &= \dfrac{h}{{mv}}\\ v &= \dfrac{h}{{m \times \lambda }} \end{align*} {/eq}


Substituting the values in the above equation as,

{eq}\begin{align*} v &= \dfrac{h}{{m \times \lambda }}\\ v &= \dfrac{{6.626 \times {{10}^{ - 34}}}}{{\left( {84} \right) \times \left( 1 \right)}}\\ v &= 7.89 \times {10^{ - 36\,}}{\rm{m/s}} \end{align*} {/eq}


Thus the velocity is {eq}v = 7.89 \times {10^{ - 36\,}}{\rm{m/s}} {/eq}


Learn more about this topic:

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Linear Velocity: Definition & Formula

from MCAT Prep: Help and Review

Chapter 14 / Lesson 12
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