Example from Physics, 22.1 The Structure of the Atom

The Structure of the Atom: example

A hydrogen atom is struck by a photon. How much energy must be absorbed from the photon to raise the electron of the hydrogen atom from its ground state to its second orbital?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
The hydrogen atom has an atomic number of Z = 1. Raising the electron from the ground state to its second orbital will increase its orbital level from n = 1 to n = 2. The energy determined will be measured in electron-volts.
Solution
The amount of energy necessary to cause the change in electron state is the difference between the final and initial energies of the electron. The final energy state of the electron can be found using

$E_{n} = \frac{Z^{2}}{n^{2}} E_{o} (n = 1, 2, 3, ...) .$
22.15

Knowing the n and Z values for the hydrogen atom, and knowing that E_o = –13.6 eV, the result is

$E_{f} = \frac{1^{2}}{2^{2}} (- 13.6 eV) = - 3.4 eV .$
22.16

The original amount of energy associated with the electron is equivalent to the ground state orbital, or

$E_{O} = \frac{1^{2}}{1^{2}} (- 13.6 eV) = −13.6 eV .$
22.17

The amount of energy necessary to change the orbital state of the electron can be found by determining the electron’s change in energy.

$Δ E = E_{f} - E_{o} = (- 3.4 e V) - (- 13.6 e V) = + 10.2 e V$
22.18

0 of 2 steps open

How did it go?

Strategy

Solution

Strategy

Solution