Minimum Uncertainty of Electron's Momentum

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In summary, the uncertainty in an electron's momentum is at least 1.05 x 10^-34 kg*m/s when its position is confined to roughly 10^-10 meters in an atom. This is derived from the equation delta(x)delta(p)>h, where h is the Planck's constant. This calculation does not involve the electron's velocity, as it is not relevant to the uncertainty in momentum.
  • #1
Pepsi24chevy
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In an atom, an electron is confined to a space of roughly 10^-10 meters. If we take this to be the uncertainty in the electron's position, what is the minimum uncertainty in its momentum?


delta(x)delta(p)>h (this is how it was derived in the previous parts to the problem)
Ok so i know px = mvx and m = 9.11X10^-31 kg and that delta px = 10^-10(px). I guess where i am stuck is, what do i do with the velocity term?
 
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  • #2
You are not asked about the velocity. You are asked about the uncertainty in momentum. So you got [itex]\Delta x \Delta p \geq \hbar[/itex] (or without the bar, depening on what version your book has).

So you know [itex]\Delta x[/itex], that was given and you are asked the minimum value [itex]\Delta p[/itex] can take without violating the inequality. You should be able to tell that immediately from the equation. Or least least without reference to other relations.
 
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  • #3
Galileo said:
You are not asked about the velocity. You are asked about the uncertainty in momentum. So you got [itex]\Delta x \Delta p \geq \hbar[/itex] (or without the bar, depening on what version your book has).
So you know [itex]\Delta x[/itex], that was given and you are asked the minimum value [itex]\Delta p[/itex] can take without violating the inequality. You should be able to tell that immediately from the equation. Or least least without reference to other relations.
am i missing some or would it be 1.05e-34J/10e-10?
 
  • #4
That's right. Simply [itex]\Delta p_{min}=\hbar/\Delta x[/itex]. What would you be missing?
 
  • #5
well the answer should be in kg*m/s that's why i feel i am missing something, but its probably just a conversion or something?
 
  • #6
The answer is in kg m/s, since that is the unit of momentum. The units of h is Js. Since J=Nm=kgm^2/s^2 you can work it out.
 

1. What is the concept of Minimum Uncertainty of Electron's Momentum?

The Minimum Uncertainty of Electron's Momentum is a fundamental principle in quantum mechanics that states that the product of the uncertainty in an electron's position and its momentum cannot be less than a certain value, known as Planck's constant divided by 4π. This means that the more precisely we know the position of an electron, the less precisely we can know its momentum, and vice versa.

2. How does the Minimum Uncertainty of Electron's Momentum affect our understanding of the behavior of electrons?

The concept of Minimum Uncertainty of Electron's Momentum has major implications for our understanding of the behavior of electrons at the quantum level. It shows that electrons do not have well-defined positions and momenta like classical particles, but rather exist as wave-like entities with a range of possible positions and momenta. This challenges our traditional understanding of particles and forces us to think about electrons in a more abstract way.

3. What is the Heisenberg Uncertainty Principle and how does it relate to the Minimum Uncertainty of Electron's Momentum?

The Heisenberg Uncertainty Principle is a broader principle in quantum mechanics that states that it is impossible to know both the position and momentum of a particle with absolute certainty. The Minimum Uncertainty of Electron's Momentum is a specific application of this principle to the case of electrons, where we can determine the minimum amount of uncertainty in the position and momentum of an electron.

4. How is the Minimum Uncertainty of Electron's Momentum related to the wave-particle duality of electrons?

The Minimum Uncertainty of Electron's Momentum is closely related to the wave-particle duality of electrons, which is the idea that electrons can exhibit both wave-like and particle-like behaviors. This principle shows that the more we try to measure the position of an electron, the more we disrupt its wave-like behavior and vice versa. This is because the act of measurement itself affects the behavior of the electron.

5. Can the Minimum Uncertainty of Electron's Momentum be overcome or avoided?

No, the Minimum Uncertainty of Electron's Momentum is a fundamental principle of quantum mechanics and cannot be overcome or avoided. It is a fundamental limit on our ability to measure and understand the behavior of electrons, and it plays a crucial role in many quantum phenomena, such as the stability of atoms and the behavior of subatomic particles.

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