Problem 8: Determine the energy associated with the innermost orbit of the hydrogen atom (n=1). (b) Determine the energy associated with the second orbit of the hydrogen atom. (c) What energy does an incoming photon possess to raise an electron from the first to the second allowed orbit of the hydrogen atom?

Solution

The energy possessed by an electron in the nth orbit is given by the equation

Where E0 = 13.6 eV

(a) For the innermost orbit, n = 1. Put this value in equation A,

The negative sign shows the nature of energy, i-e, it keeps the electron associated with the atom.

(b) To find the energy of the electron in the second orbit, put n = 2 in equation A,

This is the energy possessed by the electron in second orbit.

(c) In order to raise the electron from the 1st level to the 2nd, we must give it an amount of energy equal to the difference of energies in both levels. The difference in energies can be calculated by equations (1) and (2) above.

ΔE = -13.6 – (-3.4) = -13.6 + 3.4 = – 10.2 Ev

Therefore, the incoming incident electron must possess -10.2 eV of energy to raise the electron from orbit 1 to orbit 2.