Question

In Bohr's model of the hydrogen atom, which is no longer the standard for understanding the atom, the electron revolves around the nucleus in one of an array of available orbits. Each orbit is assigned a quantum number, n, starting with n = 1 for the orbit closest to the nucleus. The energy of an electron is inversely proportional to n squared, n².

1.Calculate the energy of an electron in the n =4 orbit. ________J

2.Calculate the energy of an electron in the n = ∞ orbit. ________J

Answer 1

Solution:

1. Equation for the energy of an electron, E_n = - 2.17 * 10^-18 * (Z^2 / n^2) joules

The energy of an electron in the n =4 orbit, n = 4, Z = 1 for the H-atom ( Atomic number)

E₄ = - 2.179 * 10^-18 (1 / 4^2) joules

     = - 1.36 * 10^-19 joules

Energy of an electron in the 4th orbit = 1.36 *10^-19 joules

2. Equation for the energy of an electron, E_n = - 2.17 * 10^-18 * (Z^2 / n^2) joules

The energy of an electron in the n = ∞ orbit, n = ∞ Z = 1 for the H-atom ( Atomic number)

E _∞ = - 2.179 * 10^-18 (1^2 / ∞ ^2) joules

     = - 2.179 * 10^-18 * (0) joules

E _∞ = 0

Energy of an electron in the n = ∞ orbit = 0 joules