Estimate the uncertainty in electron's position.

In summary, the uncertainty in the position of an electron with a velocity between 6.0×10^6 m/s and 6.7×10^6 m/s is estimated to be 0.00000000016546 m. This was calculated using the equation Δx≥ h/2π(mΔv), where h is Planck's constant, c is the speed of light, and the mass of the electron is 9.11*10^-31. The answer was marked incorrect despite using the correct velocity range, leading to confusion about the accuracy of the calculation.
  • #1
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1. Question
The speed of an electron is known to be between 6.0×10^6 m/s and 6.7×10^6 m/s . Estimate the uncertainty in its position.

Homework Equations



ΔpΔx ≥ h/2π
(mΔv) Δx ≥ h/2π (Since Δp= mΔv)

Δx≥ h/2π(mΔv)

h= 6.63*10-34 J*s
c= 3.0*108
mass of electron= 9.11*10-31

The Attempt at a Solution


(6.63*10^-34)/(2pi(9.11*10^-31)*(6.7*10^6 - (6*10^6))
= 0.00000000016546 m

Apparently this is incorrect. What am I doing wrong?
 

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  • #2
The range of velocities in that picture is different from the one in your problem.
 
  • #3
blue_leaf77 said:
The range of velocities in that picture is different from the one in your problem.
I am aware, that is why I wrote my work in the 3rd step of the post. I used my own velocity range.
 
  • #4
Steelers72 said:
Apparently this is incorrect.
Why is it not correct? Using your own velocities, I also got the same value. Do I miss something about what you actually want to figure out?
 
  • #5
blue_leaf77 said:
Why is it not correct? Using your own velocities, I also got the same value. Do I miss something about what you actually want to figure out?
I'm not sure. My answer was marked incorrect which is strange. I understand the problem and how to do it. I figured maybe my work was wrong or a small error?
 

1. What is meant by "uncertainty" in the context of an electron's position?

Uncertainty in this context refers to the range of possible positions that an electron could occupy in a given space. It is a measure of the precision or accuracy with which we can determine the exact location of an electron.

2. How is uncertainty in an electron's position estimated?

The uncertainty in an electron's position is estimated through the use of quantum mechanics calculations and principles. This involves taking into account factors such as the electron's wave function, the observer's measurement apparatus, and the Heisenberg uncertainty principle.

3. What units are typically used to measure uncertainty in an electron's position?

The units used to measure uncertainty in an electron's position are typically in angstroms (Å) or nanometers (nm). These units are commonly used in the field of quantum mechanics to measure distances on an atomic scale.

4. How does uncertainty in an electron's position impact scientific research and technology?

The uncertainty in an electron's position has a significant impact on scientific research and technology as it affects our understanding and ability to manipulate and control the behavior of electrons. It is a fundamental concept in quantum mechanics and is crucial in fields such as material science, electronics, and nanotechnology.

5. Can uncertainty in an electron's position ever be completely eliminated?

According to the Heisenberg uncertainty principle, it is impossible to know both the exact position and momentum of an electron simultaneously. This means that there will always be some level of uncertainty in an electron's position, and it cannot be completely eliminated.

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