Uncertainties in the momentum and kinetic energy of the proton?

Using the equation E = p^2/2m, you can find the kinetic energy for the given momentum value. As for the uncertainty, you can use the value you calculated for the uncertainty in momentum and plug it into the equation for uncertainty in energy, delta(E)*delta(t) >= hbar. Solving for delta(E), you should get an uncertainty in energy that is also in units of kg(m/s) but you can convert it to joules by multiplying by the speed of light squared. In summary, to find the uncertainties in momentum and kinetic energy of a proton in a tin nucleus, you can use the equations delta(x)*delta(p) >= hbar and delta(E)*delta(t) >= hbar, respectively. To
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Homework Statement


A proton in a tin nucleus is known to lie within a sphere whose diameter is about 2.2 multiplied by 10E-14 m. What are the uncertainties in the momentum and kinetic energy of the proton?

Homework Equations


delta(x)*delta(p) >= hbar
delta(E)*delta(t) >= hbar


The Attempt at a Solution



I understand the first part finding the uncertainty of the momentum, which is simply. . .

1.05E-34 J(s) / (2.2E-14 m) = 4.77E-21 kg(m/s)

I don't however, in any way understand finding the uncertainty in the kinetic energy. . . Howe are we suppose to know this if we aren't told the time (or does that matter). I know the answer should be something times E-14, but I would like to know how to modify and manipulate this equation (delta(E)*delta(t) >= hbar.

Any help would be appreciated.
 
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  • #2
I think you just need to find the kinetic energy corresponding to the momentum you have calculated.
 

Related to Uncertainties in the momentum and kinetic energy of the proton?

1. What are uncertainties in the momentum and kinetic energy of the proton?

Uncertainties in the momentum and kinetic energy of the proton refer to the potential errors or variations in measurements of these physical quantities. These uncertainties can arise due to limitations in experimental equipment and techniques, as well as inherent uncertainties in the proton's motion and behavior.

2. How are uncertainties calculated for the momentum and kinetic energy of the proton?

Uncertainties in the momentum and kinetic energy of the proton are typically calculated using statistical methods, such as error propagation or uncertainty analysis. These methods take into account the precision and accuracy of measurements, as well as any known sources of error, to determine the overall uncertainty in the measured values.

3. What is the significance of uncertainties in the momentum and kinetic energy of the proton?

Uncertainties in the momentum and kinetic energy of the proton are important to consider in scientific research and experiments because they can affect the accuracy and reliability of results. Understanding and accounting for uncertainties can help improve the precision and validity of scientific findings.

4. How do uncertainties in the momentum and kinetic energy of the proton impact our understanding of particle behavior?

Uncertainties in the momentum and kinetic energy of the proton can provide insights into the inherent randomness and unpredictability of particle behavior at the quantum level. These uncertainties are a fundamental aspect of the uncertainty principle, which states that it is impossible to measure both the position and momentum of a particle with complete accuracy.

5. Can uncertainties in the momentum and kinetic energy of the proton be reduced or eliminated?

While uncertainties in the momentum and kinetic energy of the proton cannot be completely eliminated, they can be minimized through careful experimental design and data analysis. By considering potential sources of error and improving measurement techniques, scientists can reduce uncertainties and improve the precision of their results.

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