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kinetic energy of electron and ground state of hydrogen atom An electron has a de Broglie wavelenght equal to the diameter of the Hydrogen atom

Physics Aug 19, 2020

kinetic energy of electron and ground state of hydrogen atom

An electron has a de Broglie wavelenght equal to the diameter of the Hydrogen atom.

What is the kinetic energy of the electron?

How does this energy compare to the ground state of the hydrogen atom?

Expert Solution

An electron has a de Broglie wavelength equal to the diameter of the Hydrogen atom.

What is the kinetic energy of the electron?

How does this energy compare to the ground state of the hydrogen atom?

The diameter of the hydrogen atom is about m.
The de Broglie wavelength is ,
where h is Planck's constant and p is the momentum
so,
And , where m is the mass of the electron.
So the kinetic energy of the electron is

So

The ground state energy of hydrogen atom is 13.6 eV

The kinetic energy of the electron is greater than the ground state energy of the hydrogen atom.

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