Orthogonality of 1s and 2s Orbitals of H

In summary, the task is to show that the 1s and 2s orbitals of H are orthogonal. The equations used are the orbital functions for n=1 and n=2. It is necessary to integrate over a certain range, and a hint is given to consider the quantum numbers of the wavefunctions.
  • #1
kungpaotuba
2
0

Homework Statement



show that 1s and 2s orbitals of H are orthogonal


Homework Equations



orbital functions n=1 and n=2


The Attempt at a Solution



Im asking what values(range) should i integrate the two equations into.

thank you
 
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  • #2
kungpaotuba said:
Im asking what values(range) should i integrate the two equations into.

Hi and welcome to the forums kungpaotuba :smile:

What do you think you should integrate over? Do you have any thoughts/ideas on this? The guidelines of this forum state that you need to show some work before we can help.
 
  • #3
kungpaotuba said:

Homework Statement



show that 1s and 2s orbitals of H are orthogonal


Homework Equations



orbital functions n=1 and n=2

HINT: What quantum numbers do the wavefunctions have ?
 
  • #4
Thank you for your Hint
 

What is the orthogonality of 1s and 2s orbitals of hydrogen?

The orthogonality of 1s and 2s orbitals of hydrogen refers to the mathematical property of being perpendicular or independent of each other. In other words, the 1s and 2s orbitals of hydrogen do not overlap or interact with each other, making them orthogonal.

Why is the orthogonality of 1s and 2s orbitals important in hydrogen?

The orthogonality of 1s and 2s orbitals is important in hydrogen because it allows for the accurate description of the electron distribution in the atom. This is crucial in understanding the chemical and physical properties of hydrogen and its compounds.

How is the orthogonality of 1s and 2s orbitals determined?

The orthogonality of 1s and 2s orbitals can be determined through mathematical calculations using the wavefunctions of these orbitals. The integral of the product of the two wavefunctions must equal zero for them to be considered orthogonal.

What happens if the 1s and 2s orbitals are not orthogonal in hydrogen?

If the 1s and 2s orbitals are not orthogonal in hydrogen, it would mean that they are overlapping or interacting with each other. This would result in a distorted electron distribution and inaccurate predictions of the atom's behavior.

Does the orthogonality of 1s and 2s orbitals only apply to hydrogen?

No, the concept of orthogonality applies to all atomic orbitals in any atom. However, the specific values and calculations may differ depending on the atom and its electron configuration.

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