The total energy of an electron in the first excited state of the hydrogen atom is about –3.4 eV. (a) What is the kinetic energy of the electron in this state? (b) What is the potential energy of the electron in this state? (c) Which of the answers above would change if the choice of the zero of potential energy is changed?
Given: The total energy of the electron in first excited state is − 3.4 eV .
(a)
The kinetic energy of the electron is equal to negative of the total energy in its first excited state.
K = − E = − ( − 3.4 ) = + 3.4 eV
Thus, the kinetic energy of the electron in the given state is + 3.4 eV .
(b)
The potential energy of the electron is equal to the negative of twice of its kinetic energy in its first excited state.
U = − 2 K = − 2 × ( 3.4 ) = − 6.8 eV
Thus, potential energy of the electron is − 6.8 eV .
(c)
Energy of the system depends on its state, that is, reference point, if the choice of zero potential energy is changed then the value of potential energy and total energy of the system will also change but kinetic energy does not change.
Given: The total energy of the electron in first excited state is
(a)
The kinetic energy of the electron is equal to negative of the total energy in its first excited state.
Thus, the kinetic energy of the electron in the given state is
(b)
The potential energy of the electron is equal to the negative of twice of its kinetic energy in its first excited state.
Thus, potential energy of the electron is
(c)
Energy of the system depends on its state, that is, reference point, if the choice of zero potential energy is changed then the value of potential energy and total energy of the system will also change but kinetic energy does not change.
