Chemistry Exam > Chemistry Questions > The wave function for an electron in a hydrog...
Start Learning for Free
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.?
Most Upvoted Answer
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.
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.
|
Explore Courses for Chemistry exam
|
|
Similar Chemistry Doubts
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.?
Question Description
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.? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about 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.? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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.?.
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.? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about 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.? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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.?.
Solutions for 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.? in English & in Hindi are available as part of our courses for Chemistry.
Download more important topics, notes, lectures and mock test series for Chemistry Exam by signing up for free.
Here you can find the meaning of 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.? defined & explained in the simplest way possible. Besides giving the explanation of
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.?, a detailed solution for 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.? has been provided alongside types of 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.? theory, EduRev gives you an
ample number of questions to practice 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.? tests, examples and also practice Chemistry tests.
|
|
Explore Courses for Chemistry exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup