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I'm not an expert teacher or lecturer of chemistry. I was only a student from SMA NEGERI 15 SURABAYA who had been one of the Bronze Medalist Participants of Olimpiade Sains Nasional X (2011) of Chemistry In Manado, North Sulawesi, 11 - 16 September 2011 and graduated in 2012. Now, I'm studying at Universitas Airlangga in Surabaya, Indonesia. I do love chemistry and I would like to help them who had difficulties in studying chemistry. That's why, please understand me if you found some misconcepts in my entries. Suggestions are always necessary in order to develop this blog. And I'm sorry because my English isn't so well.

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Friday, November 16, 2012

Normalization Factor of Hydrogen Atom's Orbital Wave Function

In this post, We will only discuss 1 problem about how to Normalize an orbital wave function in Hydrogen Atom. For further reference, I will try to post it in the next posts.

There's an unnormalized Hydrogen Atom's Wave Function:


Now, let's normalize that function!


Problem 1
First, you have to know about these mathematical operations:


 Where x is a variable, e is the euler number, and a is a constant (In this case: Bohr's Atomic Radius [53 pm])

Second, you also have to know that in Hydrogen Atom, we use Spherical Coordinate where the Normalization Factor must be determined by the following operation:

Where N is the normalization factor, Ψ and Ψ* is the wave function and dτ is the derivative for spherical coordinate that can be expanded as follows:


Now, Let's calculate it.

To make an easier calculation, let's separate those integrals.

First Integral:

Second Integral:
By using Substitution Integral Method, (let x = cos θ so that dx = - sin θ d θ), we will get:






Third Integral:



We already calculated those three integrals, now let's finish this problem

Thank You
 

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