Question

The ground state energy of hydrogen atom is -13.6 ev. What are the kinetic and potential energies of electron in this state ?

Answer 1

the ground state of hydrogen atom is at energy -13.6 eV.

naturally this energy value is total energy.

E = T + V where T and V ar kinetic and potential energy of the system.

This energy is the eigen value of the Hamiltonian operator in ground state.

Therefore T = E -V ; as V = -2.T

will be E = -13.6 + 2.T therefore T = +(13.6 eV)

therefore the K.E. = 13.6 eV and potential energy will be - -27.2 eV so that the ground state is at -13.6 eV.

Answer 2

Explanation:

$\Large{\pink{\underline{\underline{\sf{\blue{Solution:}}}}}}$

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Ground state energy of hydrogen atom, $\sf E\:=\:-13.6\,eV$

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$\hookrightarrow$ This is the total energy of a hydrogen atom. Kinetic energy is equal to the negative of the total energy

Kinetic energy = -E = -(-13.6) = 13.6eV

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$\hookrightarrow$ Potential energy us equal to the negative of two times of kinetic energy

Potential Energy = -2 × (13.6) = -27.2eV