Bohr's model of the hydrogen atom successfully explained emission and absorption spectra.  Not only did Bohr's model provide a conceptual description of emission and absorption spectra, it also correctly predicted the wavelength of the spectral lines in hydrogen's emission and absorption spectra.  Furthermore, Bohr's model explained why absorption lines match emission lines.

According to Bohr's model, an electron only emits or absorbs energy when it moves between energy levels.  The energy that is emitted or absorbed by an atom is in the form of a photon.

 

The amount of energy that is emitted or absorbed is the energy difference between the energy levels.

The frequency or wavelength of a photon is related to its energy. 

 

Expressed as an equation:

 

 

 

Quantity

Symbol

SI Unit

change in energy

ΔE

J or eV

initial energy

E i

J or eV

final energy

E f

J or eV



 

Expressed as an equation:

  

Quantity

Symbol

SI Unit

photon energy

E

J or eV

Planck's constant

h

6.63 × 10-34 J-s
or 4.14 × 10-15 eV-s

frequency

f

Hz

wavelength

λ

m

speed of light

c

3.00 × 108 m/s

 



























Example Problem 1. 


A photon is absorbed by a hydrogen atom, causing an electron to jump from the n = 1 energy level to the n = 3 energy level.  Using Hydrogen's energy level diagram, determine the change in energy of the electron and the wavelength of the absorbed photon.

Given

Required
the energy of the released photon and the wavelength of the photon

Analysis and Solution

The red arrow shows that an electron has made a transition from the n = 1 to the n = 3 energy level.  The change in the electron's energy that occurs as a result of the transition is as follows:

The change in the electron's energy is equal to the photon's energy, which is related to its wavelength as follows:

Paraphrase

The energy of the photon is 12.09 eV and it has a wavelength of 1.03×10-7 m.