# Obtain an expression for the energy of an electron in the nth orbit of hydrogen atom in terms of the radius of the orbit and absolute constants.

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Obtain an expression for the energy of an electron in the nth orbit of hydrogen atom in terms of the radius of the orbit and absolute constants.

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Consider an electron of mass m and charge –e revolving round the nucleus of an atom of atomic number Z in the nth orbit of radius ‘r’. Let ν be the velocity of the electron. The electron possess potential energy because it is in the electrostatic field of the nucleus it also possess kinetic energy by virtue of its motion.

Potential energy of the electron is given by Ep = (potential at a distance r from the nucleus)(-e)

Kinetic energy of the electron is given by

Ek = 1/2 mv2 --------- (2)

From Bohr’s postulate

Substituting this value of mv2 in equation (2)

Total energy of the electron resolving in the nth orbit is given by En = Ep + Ek

The radius of nth permitted orbit of the electron is given by

Substituting this value of r in equation (4).

for hydrogen like atoms.

For hydrogen atom Z = 1.

Total energy of the electron in the nth orbit of hydrogen atom is