Hydrogen atom expectation of r^2 check

Thread starter keith river
Start date Apr 23, 2011
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Atom Expectation Hydrogen Hydrogen atom

In summary, the Hydrogen atom expectation of r^2 check is a mathematical calculation used in quantum mechanics to determine the average distance between the electron and the nucleus in a hydrogen atom. This calculation is important because it provides valuable information about the electron's behavior and helps in understanding the structure and properties of atoms. The expectation of r^2 is calculated by using the wave function of a hydrogen atom, which is squared and multiplied by the distance from the nucleus squared. The resulting value is then integrated over all possible distances to find the average distance. The significance of the expectation of r^2 value lies in its ability to provide information about the stability and size of the hydrogen atom, with a larger value indicating a greater probability of finding the electron farther

Apr 23, 2011

keith river

I haven't posted any of my working for this as I only want to check my answer.

Q. For a hydrogen atom with n=2, l=1, m=0
calculate <r^2>

My answer = 0.75 * a^2

where a is the bhor radius.

Am I right?

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Apr 23, 2011

ideasrule

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I don't think that's correct; I get a much larger answer. Can you show your work?

What is the "Hydrogen atom expectation of r^2 check?"

The Hydrogen atom expectation of r^2 check is a mathematical calculation used in quantum mechanics to determine the average distance between the electron and the nucleus in a hydrogen atom.

Why is the expectation of r^2 important in the study of hydrogen atoms?

The expectation of r^2 is important because it provides valuable information about the electron's behavior in a hydrogen atom, such as the probability of finding the electron at a certain distance from the nucleus. This helps in understanding the structure and properties of atoms.

How is the expectation of r^2 calculated?

The expectation of r^2 is calculated by using the wave function of a hydrogen atom, which is a mathematical representation of the electron's behavior. The wave function is squared and then multiplied by the distance from the nucleus squared. This value is then integrated over all possible distances from the nucleus to find the average distance.

What is the significance of the expectation of r^2 value?

The expectation of r^2 value provides information about the stability and size of the hydrogen atom. A larger expectation of r^2 value indicates that the electron is more likely to be found farther away from the nucleus, while a smaller value indicates that the electron is more likely to be found closer to the nucleus.

How does the expectation of r^2 value change for different energy levels in a hydrogen atom?

The expectation of r^2 value increases as the energy level of the electron increases. This is because electrons in higher energy levels have a greater probability of being found farther away from the nucleus. This relationship is important in understanding the electronic structure of atoms.