PHYS 1010Q Lecture Notes - Lecture 34: Wave Equation, Electron Microscope

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6 Mar 2018

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An interference pattern for light (left) and electrons (right) passing by a sharp. Interference is conclusive evidence for wave-like behavior. An electron microscope makes practical use of the wave nature of electrons. The de broglie wavelength of high-speed electrons is typically thousands of times shorter than the wavelength of visible light, so the electrons are able to distinguish details not apparent with light. In this equation, the thing that waves is a mathematical entity called the wave function, notated as psi or . Probability of finding the particle i am talking about at any position or time. The wave function represents the possibilities that can occur for a system. For a particle confined in a box, the solutions to the shcr dinger wave equation are those standing waves that just fit inside the box. , p, v, ke of a particle confined in a length l. = n any n h p = .

Related Questions

An interference pattern is formed on a screen by shining a planar wave on a double-slit arrangement (left). If we cover one slit with a glass plate (right), the phases of the two emerging waves will be different because the wavelength is shorter in glass than in air. If the phase difference is 180 degrees how is the interference pattern, shown left, altered?

Ans: Bright and Dark fringes are interchanged. WHY??

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In 1924, Louis de Broglie postulated that particles such aselectrons and protons might exhibit wavelike properties. Histhinking was guided by the notion that light has both wave andparticle characteristics, so he postulated that particles such aselectrons and protons would obey the same wavelength-momentumrelation as that obeyed by light: \lambda = h/p, where lambda isthe wavelength, p the momentum, and h Planck's constant.

a. Find the de Broglie wavelength lambda for an electron moving ata speed of 1.00 \times 10^6 \; {\rm m/s}. (Note that this speed islow enough that the classical momentum formula p=mv is stillvalid.) Recall that the mass of an electron is m_{\rm e} =9.11\times 10^{-31}\; {\rm kg}, and Planck's constant is h = 6.626\times 10^{-34}\; {\rm J \cdot s}.
Express your answer in meters to three significant figures.
lambda =7.270Ã10-10 \rm m

b. Find the de Broglie wavelength lambda of a baseball pitched at aspeed of 43.7 m/s. Assume that the mass of the baseball is 0.143\;{\rm kg}.
Express your answer in meters to three significant figures
lambda =1.06Ã10-34 \rm m

c. Consider a beam of electrons in a vacuum, passing through a verynarrow slit of width 2.00 \;\mu{\rm m}. The electrons then headtoward an array of detectors a distance 1.076 m away. Thesedetectors indicate a diffraction pattern, with a broad maximum ofelectron intensity (i.e., the number of electrons received in acertain area over a certain period of time) with minima of electronintensity on either side, spaced 0.518 cm from the center of thepattern. What is the wavelength lambda of one of the electrons inthis beam? Recall that the location of the first intensity minimain a single slit diffraction pattern for light is y=L \lambda /a,where L is the distance to the screen (detector) and a is the widthof the slit. The derivation of this formula was based entirely uponthe wave nature of light, so by de Broglie's hypothesis it willalso apply to the case of electron waves.
Express your answer in meters to three significant figures.

I only need C... please answer fully, thank you

A pinhole camera has a small circular aperture of diameter(D). Light from distant objects passes through the aperture into an otherwise dark box, falling on a screen located a distance ( away. If is too large, the display on the screen will be fuzzy because a bright point in the field of view will send light onto a circle of diameter slightly larger than . On the other hand, if is too small, diffraction will blur the display on the screen. The screen shows a reasonably sharp image if the diameter of the central disk of the diffraction pattern, specified by Equation is equal to at the screen.
(a) Show that for monochromatic light with plane wave fronts and , the condition for a sharp view is fulfilled if

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PHYS 1010Q Lecture Notes - Lecture 34: Wave Equation, Electron Microscope

PHYS 1010Q Full Course Notes

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