Four lowest vibrational states of these ions

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In summary, the conversation discusses the regular arrangement of atomic ions in metals known as a crystal lattice and the movement of conduction electrons through this lattice. It also poses a question about the energies of vibrational states in a crystal consisting of aluminum ions. The attempt at a solution involves using a formula for equilibrium separation and vibrational frequency, but it resulted in incorrect values. Further details and a correction to the energy level formula are requested to determine the correct values.
  • #1
albertsmith
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Homework Statement


41.CP44.jpg

In most metals, the atomic ions form a regular arrangement called a crystal lattice. The conduction electrons in the sea of electrons move through this lattice. The figure (Intro 1 figure) is a one-dimensional model of a crystal lattice. The ions have mass m , charge e , and an equilibrium separation b.


Homework Equations


Suppose this crystal consists of aluminum ions with an equilibrium spacing of 0.30nm. What are the energies of the four lowest vibrational states of these ions?


The Attempt at a Solution


well i thought separation equilibrium = (h bar/mw)^0.5 from this i got the w angular frequency and then i use the vibrational formula (n-1)h bar * w i got these first four vibrational states 0.42ev,1.30ev,2,1ev,2,9ev but i got it wrong can anybody tell what i did wrong please thanks
 
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  • #2
You'll have to give details as to how you derived that frequency. Also, there is a problem with the formula for the energy levels.
 

Related to Four lowest vibrational states of these ions

What are the four lowest vibrational states of these ions?

The four lowest vibrational states of these ions refer to the four energy levels at which the ions are vibrating. These energy levels are typically represented as the ground state and three excited states.

Why are the four lowest vibrational states important to study?

The four lowest vibrational states are important to study because they provide valuable information about the behavior and properties of the ions. By understanding these states, scientists can gain insight into the structure, stability, and reactivity of the ions.

How are the four lowest vibrational states determined?

The four lowest vibrational states of ions are determined through experimental techniques such as spectroscopy or computational methods like quantum chemistry calculations. These methods allow scientists to measure or predict the energy levels of the ions.

Can the four lowest vibrational states of ions change?

Yes, the four lowest vibrational states of ions can change under certain conditions. For example, when the ions interact with other molecules or are exposed to different environmental conditions, their energy levels may shift. This can have an impact on the properties and behavior of the ions.

What practical applications do the four lowest vibrational states of ions have?

The four lowest vibrational states of ions have various practical applications, including in fields such as materials science, catalysis, and biochemistry. By understanding the vibrational states of ions, scientists can design and develop new materials, optimize chemical reactions, and study biological processes.

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