Uncertainty Principle and kinetic energy

In summary, the conversation discusses two problems. The first problem involves calculating the time and distance traveled by an electron with a specific speed and uncertainty, as well as the same calculations for a 1.0g insect. The second problem involves an unstable elementary particle called the eta meson, with a given rest mass and mean lifetime, and the uncertainty in its rest mass. The relevant equation mentioned is the uncertainty principle.
  • #1
tomnomnom
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Homework Statement


Hey everyone. I've been trying to figure out these two problems for a few hours now to no luck. I really have no idea where to start. Hopefully, someone can help me out.

1) a) How much time is needed to measure the kinetic energy of an electron whose speed is 10.0 m/s with an uncertainty of no more than .1%? How far will the electron have traveled in this period of time? b) Make the same calculations for a 1.0g insect whose speed is the same. What do these sets of figures indicate?

2) An unstable elemtary particle called the eta meson has a rest mass of 549 MeV/c^2 and a mean lifetime of 7.00x10^-19s. What is the uncertainty in its rest mass?
 
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  • #2
Start by listing out all relevant equations, like the uncertainty principle.
 

FAQ: Uncertainty Principle and kinetic energy

What is the Uncertainty Principle?

The Uncertainty Principle, also known as Heisenberg's 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 principle is a result of the wave-particle duality of matter, where particles can behave as both waves and particles.

How does the Uncertainty Principle relate to kinetic energy?

The uncertainty principle is closely related to the concept of kinetic energy. According to the principle, the more accurately we know the position of a particle, the less accurately we can know its momentum, and vice versa. This means that as the uncertainty in position decreases, the uncertainty in momentum increases, resulting in a larger range of possible kinetic energies for the particle.

Can the Uncertainty Principle be violated?

No, the Uncertainty Principle is a fundamental law of quantum mechanics and has been extensively tested and verified through experiments. It is considered to be one of the most well-established principles in physics.

How does the Uncertainty Principle impact our daily lives?

The Uncertainty Principle is only noticeable at the atomic and subatomic level and does not have a significant impact on our daily lives. However, it does play a crucial role in many technologies, such as transistors and lasers, that are used in modern electronics.

Is there a mathematical equation for the Uncertainty Principle?

Yes, the Uncertainty Principle is mathematically described by the famous Heisenberg Uncertainty Equation: ΔxΔp ≥ h/4π, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is the Planck constant. This equation sets a limit on the precision with which we can measure the position and momentum of a particle.

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