De Broglie's wavelength problem

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In summary: This is a very small uncertainty and shows why we cannot see the wavelike nature of the bullet using diffraction. In summary, a bullet with a mass of 40 g and a speed of 1000 m/s has a de Broglie wavelength of 1.66 x 10^-35 m. However, due to the small distance between atoms and the bullet's relatively large wavelength, we cannot observe its wavelike nature through diffraction. Additionally, the uncertainty in the bullet's position when measured simultaneously with its speed is 1.65 x 10^-37 m, which is too small to accurately detect any wavelike properties.
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fluidistic
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Hi, I would like a correction + help for the last question.

Homework Statement


A bullet of mass m=40 g travels at speed 1000 m/s.
1)What is its de Broglie wavelength?
2)Why can't we see the wavelike nature of the bullet by means of diffraction?
3)If the uncertainty of which we measured the velocity of the bullet is 0.01 m/s, determine the uncertainty of the position if we measure it simultaneously with the speed.

Homework Equations



[tex]\lambda = \frac{h}{p}[/tex] and [tex]\Delta p \Delta x \geq \frac{\hbar}{2}[/tex].

The Attempt at a Solution


1)[tex]1.66 \times 10 ^{-35 }m[/tex] using the formula I just gave.
2)Because the distance between atoms is roughly of the order of [tex]10^{-10} m[/tex] which is much greater than the wavelength of the bullet. So we could apply geometrical optics for the ray tracing of the bullet and there's absolutely no wavelike properties involved.
3)Not really sure for this one. Using Heisenberg's inequality I get [tex]\Delta x \geq \frac{\hbar}{2 \cdot 0.04 kg \cdot 0.01m}[/tex]. But with this result I do not answer the question. I think I should get something of the form [tex]\Delta x \leq ...[/tex]. Any thoughts on this one?
 
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  • #2
Answer for 3):Using Heisenberg's Uncertainty Principle, the uncertainty in position can be calculated as follows: Δx = h/2mv = 6.626 x 10^-34/(2 x 0.04 x 1000) = 1.65 x 10^-37 m
 

1. What is De Broglie's wavelength problem?

De Broglie's wavelength problem, also known as the matter-wave duality, is a fundamental concept in quantum mechanics that suggests that all particles, such as electrons and protons, have both wave-like and particle-like properties.

2. How did De Broglie's wavelength problem come about?

In 1924, French physicist Louis de Broglie proposed the idea that particles, like electrons, could have wave-like properties, based on the observation that light, which was thought to only have wave-like properties, sometimes behaved like particles.

3. What is the equation for calculating De Broglie's wavelength?

The equation for De Broglie's wavelength is λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the particle, and v is its velocity.

4. What is the significance of De Broglie's wavelength problem?

De Broglie's wavelength problem helped to solidify the concept of wave-particle duality in quantum mechanics, which has since been confirmed through numerous experiments. It also helped to bridge the gap between classical physics and the emerging field of quantum mechanics.

5. How is De Broglie's wavelength problem relevant in modern science?

The concept of De Broglie's wavelength problem is still relevant in modern science, as it is a crucial component of quantum mechanics and is used in many applications, such as electron microscopy and particle accelerators. It also continues to be studied and explored in various fields, such as quantum computing and nanotechnology.

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