Question

A) The total energy of an electron in the first excited state of the hydrogen atom is about $-3.4eV$. What is the kinetic energy of the electron in this state?

B) The total energy of an electron in the first excited state of the hydrogen atom is about $–3.4eV$. What is the potential energy of the electron in this state?

C) The total energy of an electron in the first excited state of the hydrogen atom is about $-3.4eV$. How would the value of total energy change if the choice of the zero of potential energy is changed?

Answer 1

A) As we know,
Total energy = Kinetic energy + Potential Energy
Kinetic energy(𝐾) of electron is equal to the negative of total energy(T)
$K=-T$
Given, $T=-3.4eV$
Therefore,
$K=-3(-3.4eV)$
$K=+3.4eV$
Final Anser : $K=+3.4eV$

B) As we know,
Total energy = Kinetic energy + Potential Energy
Kinetic energy(K) of electron is equal to the negative of total energy(T)
$K=-T$
Given, $T=-3.4eV$
Therefore,
$T=K+U$
$-3.4eV=(+3.4eV)+U$
$P.E=-6.8eV$
Potential energy (U) of the electron is equal to the negative of twice of its kinetic energy.
Final Answer: $P.E=-6.8eV$

C) If the zero of potential energy is chosen differently, kinetic energy does not change. Its value is independent of the choice of the zero of potential energy.
The potential energy of a system depends on the reference point taken. If the reference point is changed, then the value of the potential energy of the system also changes. Since total energy is the sum of kinetic and potential energies, total energy of the system will also change.
Final Answer: If the reference point is changed, then the value of the potential energy of the system also changes, and total energy of the system will also change.