Question about the Heisenberg Uncertainty Principle

In summary, the conversation discusses the minimum uncertainty in the speed of a particle based on its de Broglie wavelength and average speed. The solution involves using the equations for de Broglie wavelength, uncertainty in linear momentum, and uncertainty in speed to determine the minimum uncertainty in the particle's speed. The key to solving this problem is using the equation delta p = m * delta v.
  • #1
MrDMD83
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0

Homework Statement



Suppose the minimum uncertainty in the position of a particle is equal to its de Broglie wavelength. If the particle has an average speed of 4.7 105 m/s, what is the minimum uncertainty in its speed?

Homework Equations



lambda=h/p & (Py)(Y) is greater than or equal to h/4pi

The Attempt at a Solution



I'm not really sure where to start
 
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  • #2
Let LAMDA = De Broglie Wavelength
DELTAp = uncertainty in linear momentum
DELTAy = uncertainty in position
DELTAv = uncertainty in speed

(Question gives:) DELTAy = LAMDA
Since DELTAp*DELTAy = h/(4pi), then DELTAp*LAMDA = h/(4pi)
Thus, LAMDA = h/(4pi*DELTAp)

Also, LAMDA = h/p

Combine the 2: h/(4pi*DELTAp) = h/p
So: 4pi*DELTAp = p

p = mv, DELTAp = m*DELTAv
4pi*m*DELTAv = mv
4pi*DELTAv = v

We want DELTAv, so:
DELTAv = v/(4pi)

tada.
 
  • #3
oh man, delta p=m*delta v was the whole key to figuring this out that I NEVER would have thought of. Thank you so much for this detailed solution! You are the master :)
 

FAQ: Question about the Heisenberg Uncertainty Principle

1. What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle is a fundamental principle in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle. This means that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

2. Who discovered the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle was first proposed by German physicist Werner Heisenberg in 1927. Heisenberg's work was based on previous theories by Niels Bohr and Max Planck, and it revolutionized the field of quantum mechanics.

3. How does the Heisenberg Uncertainty Principle affect our understanding of the physical world?

The Heisenberg Uncertainty Principle challenges our traditional understanding of the physical world, as it suggests that it is impossible to have complete knowledge of a particle's properties at any given time. This principle has led to further advancements in quantum mechanics and has helped us better understand the behavior of particles at the subatomic level.

4. Can the Heisenberg Uncertainty Principle be applied to macroscopic objects?

No, the Heisenberg Uncertainty Principle only applies to particles at the quantum level. This is because the uncertainty in position and momentum becomes negligible for larger objects. However, the principle can still be applied to the behavior of large collections of particles, such as gases or liquids.

5. How is the Heisenberg Uncertainty Principle used in practical applications?

The Heisenberg Uncertainty Principle has been used in various practical applications, such as in the development of sensitive instruments like atomic clocks and electron microscopes. It has also been used in cryptography and information technology, as it provides a foundation for quantum computing and secure communication methods.

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