The total energy of an electron in the ground state of the hydrogen atom is about (– 13.eV). Find:
(a) What is the kinetic energy of the election in its first excited state?
(b) What is the potential energy of the electron is its first excited state?
(c) What is the total energy of the election in its first excited state?
(d) Which of the above answers would change if the choice of zero potential energy is altered?
Answers
Answer:
Bohrs model, mvr = nh and rmv2=4πε0r2Ze2, which give,
T=21mv2=8πε0rZe2;r=Ze2m4πε0h2n2
These relations have nothing to do with the choice of the zero of potential energy. Now, choosing the zero of potential energy at infinity, we have V=−(Ze2/4πε0r), which gives V=−2T and E=T+v=−T.
(a) The quoted value of E = 3.4 eV is based on the customary choice of zero of potential energy at infinity. Using E = T, the kinetic energy of the electron in this state is + 3.4 eV.
(b) Using V = 2T, potential energy of the electron is = 6.8 eV.
(c) If the zero of potential energy is chosen differently, kinetic energy does not change. Its value is + 3.4 eV independent of the choice of the zero of potential energy. The potential energy, and the total energy of the state, however, would alter if a different zero of the potential energy is chose
Explanation:
Bohrs model, mvr = nh and rmv2=4πε0r2Ze2, which give,
T=21mv2=8πε0rZe2;r=Ze2m4πε0h2n2
These relations have nothing to do with the choice of the zero of potential energy. Now, choosing the zero of potential energy at infinity, we have V=−(Ze2/4πε0r), which gives V=−2T and E=T+v=−T.
(a) The quoted value of E = 3.4 eV is based on the customary choice of zero of potential energy at infinity. Using E = T, the kinetic energy of the electron in this state is + 3.4 eV.
(b) Using V = 2T, potential energy of the electron is = 6.8 eV.
(c) If the zero of potential energy is chosen differently, kinetic energy does not change. Its value is + 3.4 eV independent of the choice of the zero of potential energy. The potential energy, and the total energy of the state, however, would alter if a different zero of the potential energy is chose