Probability of a measured energy for a hydrogen atom

In summary, the probability of measuring a specific energy for a hydrogen atom is determined by the energy level of the electron and can be calculated using the Schrödinger equation. This probability does not change over time, but can be altered by external influences or interactions with other particles. The uncertainty principle also affects the probability, as the more precisely the momentum is known, the less certain we can be about the energy and vice versa.
  • #1
reminiscent
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Homework Statement


https://imgur.com/a/8deZc

Homework Equations


P(E) = ∫φ*(r)ψ(r)dr from -∞ to ∞

The Attempt at a Solution


To find the probability, I know I have to use this equation:

P(E) = ∫φ*(r)ψ(r)dr from -∞ to ∞

My question is, what is the energy eigenstate, φ*(r)? Is it the measured energy they gave us? I don't have a full understanding of this.
If it is the measured energy, integrating it would just give me 0.
Thank you.
 
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  • #2
You'll have to find the wave function that corresponds to the given energy eigenstate.
 

FAQ: Probability of a measured energy for a hydrogen atom

1. What is the probability of measuring a certain energy for a hydrogen atom?

The probability of measuring a specific energy for a hydrogen atom depends on the energy level of the electron in the atom. According to the Bohr model, the energy levels of a hydrogen atom are discrete and can be represented by the equation E = -13.6/n2, where n is the principal quantum number. The probability of measuring a particular energy is proportional to the square of the wavefunction, which is determined by the quantum numbers of the electron.

2. How is the probability of a measured energy for a hydrogen atom calculated?

The probability of a measured energy for a hydrogen atom can be calculated using the Schrödinger equation, which describes the wave-like behavior of particles at the quantum level. By solving this equation for the hydrogen atom, the wavefunction can be determined and the probability of measuring a certain energy can be calculated.

3. Does the probability of a measured energy for a hydrogen atom change over time?

No, the probability of a measured energy for a hydrogen atom does not change over time. This is because the energy levels of the hydrogen atom are fixed and do not vary with time. However, the probability of finding the electron in a specific energy level may change if the atom is exposed to external influences, such as an electric or magnetic field.

4. How does the uncertainty principle affect the probability of a measured energy for a hydrogen atom?

The uncertainty principle, which states that the position and momentum of a particle cannot be simultaneously known with absolute certainty, affects the probability of a measured energy for a hydrogen atom. This is because the wavefunction of the electron, which determines the probability of finding it at a certain energy level, is related to its momentum. Therefore, the more precisely the momentum is known, the less certain we can be about its energy and vice versa.

5. Can the probability of a measured energy for a hydrogen atom be altered?

The probability of a measured energy for a hydrogen atom can be altered by changing the conditions of the atom. For example, by applying an external electric or magnetic field, the energy levels of the atom can be shifted and therefore change the probability of measuring a certain energy. Additionally, the probability can also be affected by interactions with other particles, such as collisions with other atoms or particles.

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