Find the De Broglie wavelength

In summary, Johnny Jumper's favorite trick is to fall 56.0 meters into a pool from his high-rise window. A news reporter captured a photo of him right before he hit the water, with a shutter speed of 7.00 milliseconds. To find Johnny's de Broglie wavelength at this moment, the equation wavelength = h / (mv) is used, with a known mass of 70 kg and calculated velocity of 8000 m/s. However, this approach may not be accurate for calculating his speed at impact. Instead, the equation v^2=2gs can be used to calculate his kinetic energy at that point. The role of the shutter speed in this calculation is unclear.
  • #1
SamTsui86
31
0

Homework Statement



Johnny Jumper's favorite trick is to step out of his high-rise window and fall 56.0 m into a pool. A news reporter takes a picture of 70.0 kg Johnny just before he makes a splash, using an exposure time of 7.00 ms. Find the following.

(a) Johnny's de Broglie wavelength at this moment

Homework Equations



wavelength = h / (mv) v = x/t

The Attempt at a Solution



so I know figured out v which is just 56 m / .007 s = 8000 m/s
I know m = 70 kg
I plug it into the equation wavelength = (6.63e-34) / ((8000)(70)))

I got 1.18e-39 m. It saids I am wrong, please help
 
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  • #2
I'm slightly confused by your first step in which you divide the 56 meter height of the building by the camera's shutter speed to come at 8 thousand meters per second.

If you are trying to calculate his speed at impact, this is not the right way to do it.
 
  • #3
You can calculate his speed but using: [tex] v^2=2gs, (u^2=0[/tex] in this case). You can use [tex]\lambda=\frac{h}{\sqrt{2mT}}[/tex] where T is the kinetic energy of the man at that point.

The virtue of using [tex]v^2[/tex] for this equation is that you can use it directly to calculate the kinetic energy. I think that's it, though I don't know how the shutter speed plays in. The man is accelerating with 'g' at that point if it helps though.
 

1. What is the De Broglie wavelength?

The De Broglie wavelength is a concept in quantum mechanics that states that all matter, including particles such as electrons and protons, have a wave-like nature. It is named after French physicist Louis de Broglie.

2. How do you calculate the De Broglie wavelength?

The De Broglie wavelength can be calculated using the formula λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the particle, and v is the velocity of the particle.

3. What is the significance of the De Broglie wavelength?

The De Broglie wavelength helps us understand the wave-particle duality of matter and how particles can behave as both waves and particles. It also allows us to make predictions about the behavior of particles at the quantum level.

4. Can the De Broglie wavelength be observed?

No, the De Broglie wavelength is a theoretical concept and cannot be directly observed. However, its effects can be observed in experiments such as the double-slit experiment, where particles exhibit wave-like behavior and create an interference pattern.

5. How does the De Broglie wavelength relate to the uncertainty principle?

The De Broglie wavelength is related to the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. The De Broglie wavelength is a measure of the momentum of a particle, so the more accurately we know its momentum, the less we know about its position.

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