Solve Electron Probability Density for Temp.

In summary, the ground state energy of an electron bound to a single hydrogen atom is -13.6 eV, and the energy of the first excited state is -10.2 eV. The degeneracy of the ground state is 1 and the degeneracy of the first excited state is 4. Using the Boltzmann distribution and the known value of k, the temperature required for the fraction of electrons in one specific orbital of the first excited state to be equal to the fraction of electrons in the ground state can be calculated.
  • #1
George Mahone
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[SOLVED] Probability Density

Consider a gas made of single hydrogen atoms (not diatomic hydrogen gas). The ground state energy of an electrons bound to a single hydrogen atom is -13.6 eV, and the energy of the first excited state is -10.2 eV. Ignoring the spin of the electron, the degeneracy of the ground state is 1, but the degeneracy of the first excited state if 4. (Note also that k = 8.617*10^-4 eV/K). What temperature would be required in order for the fraction of electrons in one specific orbital of the first excited states to be equal to the fraction of electrons in the ground state?I thought perhaps the electron probability densities would follow a canonical distribution, but that seems to be impossible.
 
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  • #2
I'm not sure what a 'canonical' distribution is, but they do follow a 'boltzmann' distribution.
 
  • #3
canonical = Gaussian?
 

FAQ: Solve Electron Probability Density for Temp.

What is electron probability density?

Electron probability density is a measure of the likelihood of finding an electron at a given location in an atom or molecule. It is represented by a continuous function that describes the probability of finding an electron within a small volume of space.

How is electron probability density calculated?

Electron probability density is calculated using the Schrodinger equation, which is a mathematical equation that describes the behavior of electrons in atoms and molecules. The equation takes into account the electron's mass, energy, and position, and can be solved using various mathematical techniques.

What factors affect electron probability density?

The main factors that affect electron probability density are the electron's energy level, the size of the atom or molecule, and the presence of other charged particles. Higher energy levels and larger atomic or molecular sizes generally result in higher electron probability density, while the presence of other charged particles can alter the electron's behavior and distribution.

Why is electron probability density important?

Understanding electron probability density is crucial in predicting the properties and behavior of atoms and molecules. It allows scientists to determine the likelihood of electrons being in certain locations and to make predictions about chemical reactions and the stability of different molecular structures.

How does temperature affect electron probability density?

Temperature can affect electron probability density in a few ways. Higher temperatures can increase the energy of electrons, causing them to move more quickly and potentially occupy a larger space. In addition, temperature can also affect the behavior of other charged particles, which can in turn influence the distribution of electrons. Ultimately, temperature can impact the overall electron probability density by altering the energy level and movement of electrons within an atom or molecule.

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