Finding Energy with the Uncertainty Principle

In summary, the conversation discusses using the uncertainty principle to determine the energy required for an electron to be confined inside a hydrogen atom. The radius of the atom, 1 x 10^-10 m, is used for Δr. The equation for the uncertainty principle is given, with x representing position and p representing momentum. The solution involves finding the kinetic energy of the electron, using the given radius for Δx and the mass and velocity of an electron for p. The final answer should be expressed in eV, rounded up to the nearest hundredth.
  • #1
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Homework Statement



Using the uncertainty principle find the energy required for the electron to be confined inside the hydrogen atom. Use the radius of the atom 1 x 10^-10 m for Δr. Express your answer in eV, rounded up to the nearest hundredth.

Homework Equations



Δx(Δp)[tex]\geq[/tex]h/4pie
x= position in space
p= momentum (mass)(velocity)

The Attempt at a Solution



ok I am not sure how Δr (radius) goes into the uncertainty principle, i know how it works and how it shows that it can not be exactly precise but i just don't understant how Δr would fall in the equation

is it just 1 x 10^-10 m[tex]\geq[/tex]4.14x10^-15 eV/12.56637061?
 
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  • #2
delta_r is your delta_x.

The speed of the electron is not relativistic. (at least I don't remember it to be)
Use the momentum to get your kinetic energy.
Then convert units.
 
  • #3
o ok. and for the momentum. would i just use mass and velocity of an electron?
 

1. What is the uncertainty principle?

The uncertainty principle is a fundamental principle in quantum mechanics that states that it is impossible to know both the exact position and momentum of a particle at the same time. This means that the more precisely we know the position of a particle, the less we know about its momentum, and vice versa.

2. Who discovered the uncertainty principle?

The uncertainty principle was first proposed by German physicist Werner Heisenberg in 1927. Heisenberg's work was based on previous studies done by Niels Bohr, Max Born, and Pascual Jordan.

3. How does the uncertainty principle affect our understanding of the world?

The uncertainty principle challenges our classical understanding of the world, where we assume that objects have definite properties and can be measured with absolute precision. It shows that at the subatomic level, things are more uncertain and unpredictable. It also has implications for the measurement of physical quantities and the limitations of scientific knowledge.

4. Can the uncertainty principle be violated?

No, the uncertainty principle is a fundamental principle of quantum mechanics and has been extensively tested and confirmed through experiments. It is a core principle that helps us understand the behavior of particles at the subatomic level.

5. How is the uncertainty principle relevant to everyday life?

The uncertainty principle may seem like an abstract concept, but it has practical applications in fields such as technology, medicine, and cryptography. For example, it is used in MRI machines and electron microscopes, and in the development of secure communication systems. It also has implications for the behavior of matter and energy in the universe, leading to the development of theories such as the multiverse theory.

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