What is the energy of a hydrogen atom in a mixed state?

In summary, a single hydrogen atom in a mixed state with a wave function of Ψ=(1/√2) Ψ_100+(1/√2) Ψ_200 will have an energy of E=(1/2)*13.6+(1/2)*(3.4)=8.5 eV. However, this does not correspond to a spectral line at 8.5 eV because the state is a superposition state and not an eigenstate of energy. Repeated energy measurements on atoms in this state will result in either 13.6 eV or 3.4 eV, with an average of 8.5 eV, known as the expectation value of energy. Therefore
  • #1
beman
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Suppose a single hydrogen atom is in mixed state.
Ψ=(1/√2) Ψ_100+(1/√2) Ψ_200
Then energy will be E=(1/2)*13.6+(1/2)*(3.4)=8.5 eV.
But there is no spectral line at 8.5 eV.
 
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  • #2
The state you have there is a superposition state, which is not the eigenstate of energy. Therefore, if you run a series of energy measurement to the H atoms all prepared to be in that state, you won't get a fixed value during the repeated measurements. The possible values you can get is 13.6 eV and 3.4 eV. Furthermore, if you take the average of these measurements, given large number of measurements, you will get what is called the expectation value of energy, whose value has been calculated by you to be 8.5 eV. To emphasize, 8.5 eV is not among the possibly measured energies, and hence the corresponding frequency will not appear in your spectrometer.
 
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Related to What is the energy of a hydrogen atom in a mixed state?

1. What is a hydrogen atom in mixed state?

A hydrogen atom in mixed state refers to a state in which the electron of the atom is in a superposition of two or more energy levels, rather than being in a single defined energy level. This is a phenomenon described by quantum mechanics, where the electron has a probability of being in different energy levels simultaneously.

2. How is a hydrogen atom in mixed state different from a regular hydrogen atom?

A regular hydrogen atom has an electron that is in a single defined energy level, while a hydrogen atom in mixed state has an electron that is in a superposition of energy levels. This means that the electron of a hydrogen atom in mixed state has a higher degree of uncertainty in terms of its location and energy compared to a regular hydrogen atom.

3. What causes a hydrogen atom to be in a mixed state?

A hydrogen atom can be put into a mixed state through various methods, such as exposing it to a magnetic field or using lasers to manipulate the energy levels of the electron. The exact cause depends on the experimental setup and the desired outcome.

4. What are the potential applications of a hydrogen atom in mixed state?

The ability to manipulate and control the energy levels of a hydrogen atom in mixed state has potential applications in quantum computing, where the superposition of energy levels can be used to store and process information. It can also be used in precision measurements and in studying the behavior of atoms in extreme environments.

5. Can other atoms be in a mixed state like hydrogen?

Yes, other atoms can also be in a mixed state, not just hydrogen. In fact, any atom or particle that exhibits wave-like behavior, such as electrons, protons, and neutrons, can be in a mixed state. This is one of the fundamental principles of quantum mechanics and has been observed in various experiments.

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