De Broglie Wavelength problem

In summary, the problem involves finding the de Broglie wavelength of a fullback running the 40-yd dash at a speed of 19.6 ± 0.1 mi/h and a mass of 220lbs. Using the formula λ=h/(mu), where h=6.626 x 10^(-34) kgm^2)/s, m=mass (kg), and u= speed, the calculated wavelength is 5.847 x 10^-41 m. The given answer in the book is incorrect due to a conversion error.
  • #1
grapejellypie
13
0

Homework Statement


A 220lb fullback runs the 40-yd dash at a speed of 19.6 ± 0.1 mi/h. What is he de Broglie wavelength (in meters)?


Homework Equations


de Broglie Wavelength: λ=h/(mu), where λ=wavelenght, h=6.626 x 10^(-34) kgm^2)/s, m=mass (kg), and u= speed


The Attempt at a Solution


u=19.6 m/s x (1m / 0.6214mi) x (3600s / 1h) = 113550 m/s

m= 220lb x (0.4536kg/ 1lb) = 99.792kg

λ= [6.626 x 10^(-34) kgm^2)/s] / [99.792kg x 113550 m/s]
=5.847 x 10^-41 m (MY ANSWER)

The answer in the back of the book is 7.6 x 10^-37 m
 
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  • #2
1m / 0.6214mi

This conversion is incorrect 1 km = 0.6241 miles.
 
  • #3
u=19.6 m/s x ...

Recheck the units here.
 

1. What is the De Broglie Wavelength problem?

The De Broglie Wavelength problem refers to the question of whether particles, such as electrons, can also exhibit wave-like behavior. This idea was proposed by Louis de Broglie in 1924 and was later confirmed by experiments.

2. What is the significance of the De Broglie Wavelength?

The De Broglie Wavelength is significant because it helps explain the wave-particle duality of matter. It suggests that all particles, not just light, can exhibit both wave-like and particle-like properties.

3. How is the De Broglie Wavelength calculated?

The De Broglie Wavelength is calculated using the equation 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. This equation shows that the wavelength decreases as the mass or velocity of the particle increases.

4. What is the relationship between the De Broglie Wavelength and the uncertainty principle?

The De Broglie Wavelength is related to the uncertainty principle, which states that the more precisely we know the position of a particle, the less precisely we know its momentum, and vice versa. This is because the De Broglie Wavelength is inversely proportional to the momentum of a particle.

5. How does the De Broglie Wavelength impact our understanding of the atomic and subatomic world?

The De Broglie Wavelength has greatly impacted our understanding of the atomic and subatomic world. It has helped explain the behavior of particles, such as electrons, in the quantum realm and has been fundamental in the development of quantum mechanics. It has also led to the discovery of new particles and has furthered our understanding of the fundamental nature of matter.

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