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The de Broglie wavelength of a moving particle is equal to Planck s constant divided by the particle s momentum

According to de Broglie, particles such as electrons and protons should show wavelike properties Effects such as diffraction and interference had never been observed for particles, so de Broglie s work was greeted with considerable doubt In 1927, however, the results of two independent experiments proved that electrons are diffracted just as light is In one experiment, English physicist George Thomson aimed a beam of electrons at a very thin crystal Atoms in crystals are arrayed in a regular pattern that acts as a diffraction grating Electrons diffracted from the crystal formed the same patterns that X rays of a similar wavelength formed Figure 27-9 shows the pattern made by diffracting electrons In the United States, Clinton Davisson and Lester Germer performed a similar experiment using electrons reflected and diffracted from thick crystals The two experiments proved that material particles have wave properties The wave nature of objects you see and handle every day is not observable because their wavelengths are extremely short For example, consider the de Broglie wavelength of a 0145-kg baseball when it leaves a bat with a speed of 38 m/s =

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Now let s continue, and start drawing the head. Add these lines to the drawRect: method, toward the end but still before the [NSGraphicsContext restoreGraphicsState] call:

Figure 27-9 Electron diffraction patterns, such as this one for a cubic zirconium crystal, demonstrate the wave properties of particles

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You can use more than one option within the command line, but any values associated with the command-line option must be included after the specific command-line option For example:

This wavelength is far too small to have observable effects As you will see in the following Example Problem, however, an extremely small particle, such as an electron, has a wavelength that can be observed and measured

De Broglie Wavelength An electron is accelerated by a potential difference of 75 V What is its de Broglie wavelength

Include the positive and negative plates in your drawing Known:

NSRect hRect = CGRectInset([self bounds],20,20); NSBezierPath *head = [NSBezierPath bezierPathWithOvalInRect:hRect]; NSGradient *faceGradient = [[NSGradient alloc] initWithStartingColor:[NSColor whiteColor] endingColor:[NSColor lightGrayColor]]; [faceGradient drawInBezierPath:head angle:45]; [head setLineWidth:3]; [head stroke];

Unknown:

911 10 663 10

Write relationships for the kinetic energy of the electron based on potential difference and motion and use them to calculate the electron s velocity KE

75 V

2qV m 2( 160 10 911 10

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Here we are once again using CGRectInset to make a new rect that is smaller than our bounds, this time to create an oval shape for Mr Smiley s head. After creating a Bezier path, we create something new, an instance of NSGradient, which knows how to take two or more colors and draw a smooth gradient between them. In this example, you see that it can draw itself across the inner surface of a Bezier path. Build & Run this code, and you ll see that our view now contains a round head with a shaded gradient (Figure 13 5).

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51 106 m/s Solve for momentum, p p mv (911 10 31 kg)(51 106 m/s) 46 10 24 kg m/s Solve for the de Broglie wavelength,

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Now all that s left is to draw the facial features (a simple mouth and eyes). Add these lines to the end of drawRect: (but before the final [NSGraphicsContext restoreGraphicsState] call):

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Are the units correct Dimensional analysis on the units verifies m/s for v and nm for Do the signs make sense Positive values are expected for both v and Are the magnitudes realistic The wavelength is close to 01 nm, which is in the X-ray region of the electromagnetic spectrum

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