# Solving for Energy & Momentum in Physics Questions

• anto
In summary, the first question asked if 0.5 A is the answer for the Heisenberg uncertainty principle. The second question is about finding the smallest kinetic energy of an electron which can be used to achieve the resolution of classical optics.
anto
Homework Statement
1)for an object of size 0.5 Angstrom, what is the longest-wavelength photon with which it can be observed?
2)for the object of problem 1, what is the smallest-energy electron which can be used to make the measurement?
Relevant Equations
∆E∆t = h/4(phi)
∆p∆x = h/4(phi)
∆λ = (∆E/E)λ
for the first question, i thougth that 0,5 A is the answer?

for the second question:
i used the E =hc/λ to found the E. but i got a little confused which equations to find ∆E, since there's no ∆t. or should i search the momentum, then use the λ= h/p ?

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Your title "Uncertainty principle -- Using photons vs. electrons to observe a very small object" is confusing since the HUP has absolutely nothing to do with how things are observed. That is, the HUP is in no way a measurement problem, it is a feature of reality.

Steve4Physics and weirdoguy
anto said:
for the second question:
i used the E =hc/λ to found the E. but i got a little confused which equations to find ∆E, since there's no ∆t. or should i search the momentum, then use the λ= h/p ?
Hi @anto. Welcome to PF.

As already noted by @phinds, the question has nothing to do with Heisenberg’s uncertainty principle. It’s about applying the diffraction limit of ‘classical optics’.

Your answer to the first part is reasonable. You might want to add ‘the order of‘ or ‘approximately’ to your value. If you wanted a more precise value, you could use what is called the Abbe limit (e.g. see https://en.wikipedia.org/wiki/Diffraction-limited_system#The_Abbe_diffraction_limit_for_a_microscope).

But the questions seems badly worded, I think the real questions are these:

Q1. What is the longest wavelength [of any type of wave] which can be used to resolve points separated by 0.5 Angstrom?

Q2 What is the smallest kinetic energy of an electron which can be used to achieve this resolution?
________________
You have answered Q1. For Q2, note that E = hc/λ is for photon energy, not the kinetic energy of an electron.

Q2 asks for the electron’s kinetic energy which makes the electron’s deBroglie wavelength equal to 0.5 Angstrom (or whatever your answer to Q1 is).

Can you work out a formula for the electron’s kinetic energy (E) in terms of it mass (m), its deBroglie wavelength (λ) and Planck’s constant (h)?

Edit - typo' corrected.

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## 1. What is energy and momentum in physics?

Energy and momentum are two fundamental concepts in physics that describe the motion and interactions of objects. Energy is the ability to do work or cause change, while momentum is a measure of an object's motion.

## 2. How do you solve for energy and momentum in physics?

To solve for energy and momentum in physics, you need to use relevant equations and apply the principles of conservation of energy and momentum. This involves identifying the initial and final states of a system and calculating the changes in energy and momentum between them.

## 3. What are the units of energy and momentum in physics?

The SI unit for energy is joules (J), while momentum is measured in kilogram-meters per second (kg·m/s). However, in some cases, other units such as electron volts (eV) and newton-seconds (N·s) may also be used.

## 4. How are energy and momentum related in physics?

Energy and momentum are related through the principle of conservation of energy and momentum, which states that in a closed system, the total energy and momentum remain constant. This means that energy can be converted into momentum and vice versa.

## 5. What are some real-world applications of solving for energy and momentum in physics?

Solving for energy and momentum is essential in understanding and predicting the motion and interactions of objects in various real-world scenarios. Some examples include calculating the energy and momentum of a moving car, determining the trajectory of a projectile, and analyzing collisions between objects.

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