Percent uncertainty of momentum

In summary, the question asks for the percentage of uncertainty in the momentum of a 1KeV electron, given that its position is known within 1Angstrom. Using the uncertainty principle, we can calculate the minimum uncertainty in momentum to be 5.275x10^-25 kgm/s. To find the percentage of uncertainty, we can use the formula Δp/p = .031 or 3.1%. This can also be calculated by finding the velocity using the electron's kinetic energy and then finding the momentum using the mass and velocity. Both methods result in a percentage of uncertainty of 3.1%.
  • #1
dangsy
15
0

Homework Statement


The position and momentum of a 1KeV electron are simultaneously determined. If its position is located to within 1Angstrom (Δx), what is the PERCENTAGE of uncertainty in its momentum?

Homework Equations


ΔxΔp >= h(bar)/2

The Attempt at a Solution


Δx = 1A = 1x10^-10m
Δp>= h(bar)/2Δx
Δp = 1.055x10^-34(kg/m^2)/s
-------------------------
2(1x10^-10m)
= 5.275x10^-25 kgm/s

how do I get the percentage of uncertainty?
 
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  • #2
([itex]\Delta[/itex]p/p)100.

Use the energy to find p.
 
  • #3
Thanks!

Here's what I did...
(I don't know how to use latex =/ )

KE = 1/2 mv^2
1 x10^3 eV = 1.602 x10^-16 J
1.602 x10^-16 J = 1/2 (9.1 x10^-31 kg) (v^2)
Sqrt[(2 (1.602 x10^-16 J))/(9.1 x10^-31 kg)] = v
v = 1.88 x10^7 m/s
p = mv
p = (9.1 x10^-31 kg) (1.88 x10^7 m/s)
p = 1.708 x10^-23 Kgm/s
Δp/p = .031 = 3.1 %

or click the attachment=)
 

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Related to Percent uncertainty of momentum

What is percent uncertainty of momentum?

The percent uncertainty of momentum is a measurement of the amount of uncertainty or error in the calculation of an object's momentum. It is expressed as a percentage and indicates the degree of confidence in the calculated value.

How is percent uncertainty of momentum calculated?

Percent uncertainty of momentum is calculated by taking the absolute uncertainty (the difference between the maximum and minimum possible values) and dividing it by the calculated value of momentum. This value is then multiplied by 100 to get the percentage.

Why is percent uncertainty of momentum important?

Percent uncertainty of momentum is important because it provides information about the accuracy and reliability of a measurement. It allows scientists to assess the level of uncertainty in their data and make decisions about its usefulness for their research or experiments.

What factors can contribute to percent uncertainty of momentum?

There are several factors that can contribute to percent uncertainty of momentum, including measurement errors, limitations of the measuring instruments, and the precision of the data. Environmental factors such as air resistance and friction can also affect the accuracy of the calculated momentum.

How can percent uncertainty of momentum be reduced?

To reduce percent uncertainty of momentum, scientists can use more precise measuring instruments, take multiple measurements and average them, and minimize environmental factors that can affect the accuracy of the data. It is also important to record and report the uncertainties associated with the measurements to give a more accurate representation of the data.

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