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The wave function for an electron in a hydrogen atom is sai =Ne^-r/a. Here r is the distance from the distance from nucleus to the electron and a is the bones radius. Calculate naormailsation factor,N.?
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The wave function for an electron in a hydrogen atom is sai =Ne^-r/a. ...
Calculation of Normalization Factor (N) for Wave Function in Hydrogen Atom

The wave function for an electron in a hydrogen atom is given as:

ψ = Ne^(-r/a)

where r is the distance from the nucleus to the electron and a is the Bohr radius.

Normalizing Wave Function

To normalize the wave function, we need to ensure that the total probability of finding the electron in the entire volume of the atom is equal to 1. This means that the integral of the square of the wave function over all space should be equal to 1.

∫│ψ│^2 dV = 1

where dV is the volume element in spherical coordinates.

Substituting Wave Function

Substituting the given wave function into the above equation, we get:

∫│Ne^(-r/a)│^2 dV = 1

Simplifying this equation, we get:

N^2 ∫e^(-2r/a) r^2 sinθ dr dθ dφ = 1

where θ and φ are the spherical angles.

Solving Integration

Solving the above integral gives:

N^2 (4π/3) a^3 = 1

Therefore, the normalization factor N is given as:

N = (3/4πa^3)^(1/2)

This is the required normalization factor for the wave function in a hydrogen atom.
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The wave function for an electron in a hydrogen atom is sai =Ne^-r/a. Here r is the distance from the distance from nucleus to the electron and a is the bones radius. Calculate naormailsation factor,N.?
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