How accurately can the position of a 2.7keV electron be measured?

In summary, to accurately measure the position of a 2.70keV electron, assuming its energy is known to 3.00%, you can use the equation (deltaX)(deltaE)>=h/2pi. To convert the uncertainty in energy to uncertainty in momentum, you can use the speed of the electron. Then, using the mass and velocity of the electron, you can plug in the values to the equation to find the uncertainty in position. It is recommended to use SI units to avoid unit conversion issues.
  • #1
ronpaulkid
8
0

Homework Statement



How accurately can the position of a 2.70keV electron be measured assuming its energy is known to 3.00%?

The answer is (deltaX)>=?

Homework Equations



(deltaX)(deltaP)>=h/2pi

(deltaX)(deltaE)>=h/2pi

The Attempt at a Solution



My attempt at this solution was first trying to calculate deltaX using each of the two equations listed above. I was not able to cancel out the units correctly which leads me to believe that the mass of the electron is somehow included (9.11*10^-31 kg).
 
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  • #2
Your second equation is incorrect; it should be [tex]\Delta t \cdot \Delta E \ge \frac{h}{2 \pi}[/tex]

Using the first equation, you need to know the uncertainty in momentum, but you're given the uncertainty in energy. How can you convert?
 
  • #3
use the 2.7 keV energy to find the speed of electron

now find [tex]\Delta v[/tex]

you know mass and [tex]\Delta v[/tex] of electron now

just use eqn 1

and the best way to save yourself form unit's trouble is to use SI units ... that way [tex]\Delta x[/tex] will be in metres (m)
 

Related to How accurately can the position of a 2.7keV electron be measured?

1. How is the position of a 2.7keV electron measured?

The position of a 2.7keV electron can be measured using various techniques such as electron microscopy, scanning tunneling microscopy, and x-ray diffraction. These methods involve using instruments that can detect and measure the position of the electron.

2. What is the accuracy of measuring the position of a 2.7keV electron?

The accuracy of measuring the position of a 2.7keV electron depends on the technique and instrument used. Generally, the accuracy can range from nanometers to angstroms, which is a very small scale. The accuracy can also be affected by external factors such as temperature and electromagnetic fields.

3. Can the position of a 2.7keV electron be measured with 100% accuracy?

No, it is not possible to measure the position of a 2.7keV electron with 100% accuracy. This is due to the limitations of the instruments and techniques used, as well as the inherent uncertainty principle in quantum mechanics. However, the accuracy can be improved by using advanced techniques and instruments.

4. How does the energy of the electron affect the accuracy of its position measurement?

The energy of the electron does not directly affect the accuracy of its position measurement. However, higher energy electrons tend to have shorter wavelengths and can interact differently with the measuring instruments, which can affect the accuracy of the measurement. Additionally, higher energy electrons can also be more susceptible to external forces, making it more challenging to accurately measure their position.

5. Are there any limitations to accurately measuring the position of a 2.7keV electron?

Yes, there are limitations to accurately measuring the position of a 2.7keV electron. These limitations include the resolution and sensitivity of the instruments used, as well as external factors such as temperature and electromagnetic fields. In addition, the inherent uncertainty principle in quantum mechanics also places a fundamental limit on the accuracy of the measurement.

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