This would enable students to explain the emission spectrum of hydrogen using the Bohr model of the hydrogen atom; calculate the energy, wavelength, and frequencies involved in the electron transitions in the hydrogen atom; relate the emission spectra to common occurrences like fireworks and neon lights; and describe the Bohr model of the atom and the inadequacies of the Bohr model.

1. Emission Spectrum of Hydrogen,
and Dual Nature of Matter
Prepared by: Mrs. Eden C. Sanchez

2. Learning Objectives:
1. Explain the emission spectrum of hydrogen
using the Bohr model of the hydrogen atom
2. Calculate the energy, wavelength, and
frequencies involved in the electron
transitions in the hydrogen atom.
3. Relate the emission spectra to common
occurrences like fireworks and neon lights.
4. Describe the Bohr model of the atom and the
inadequacies of the Bohr model.

3. Learning Objectives:
5. Explain the wave-particle duality of matter

4. Keywords
a. Emission spectrum
b. Rydberg’s constant
c. Ground state
d. Ground energy level
e. Excited state
f. Excited energy level
g. Travelling wave
h. Standing wave
i. De Broglie Equation

5. THE EMISSION SPECTRUM AND THE BOHR
THEORY OF THE HYDROGEN ATOM
 When elements are energized by heat or other
means, they give off a characteristic or
distinctive spectrum, called an emission
spectrum, which can be used to differentiate
one element from another.
 While scientists recognized the usefulness of
emission spectra in identifying elements, the
origins of these spectra were unknown.

6.  From Rutherford’s theory, the atom was
described to be mostly empty space having a
very tiny but dense nucleus that contained the
protons. The electrons whirled around the
nucleus in circular orbits at high velocities.

7.  Classical mechanics and electromagnetic
theory explained that any charged particle
moving on a curved path would emit
electromagnetic radiation. This implies that
electrons would lose energy and spiral into the
nucleus.

8.  In 1913, Niels Bohr proposed his model of the
hydrogen atom to explain how electrons could
stay in stable orbits around the nucleus.
 This model is no longer considered to be
correct in all its details. However, it could
explain the phenomenon of emission spectra.
 For his model of the hydrogen atom, Bohr
made the following postulates:

9. a. Electrons go around the nucleus in circular
orbits. However, not all circular orbits are
allowed. The electron is allowed to occupy
only specific orbits with specific energies.
Therefore, the energies of the electron are
quantized.
b. If the electron stays in the allowed orbit, its
energy is stable. It will not emit radiation and
it will not spiral into the nucleus.

10. c. If an electron jumps from one orbit to
another, it will absorb or emit energy in
quanta equal to ∆E = hv
h(Planck’s constant) = 6.626 X 10-34 J s

11.  According to Bohr, the energy of the electron
in the H atom is given by:
 The negative sign is an arbitrary convention. A
free electron is arbitrarily considered to have
an energy of zero. A negative energy means
that the energy of the electron is lower than the
energy of a free electron.

12.  RH is the Rydberg constant for hydrogen
equal to 2.18 x 10-18J.

13. Exercises
1. What is the energy of the electron when it is
in the first orbit, n=1?
2. What is the energy of the electron in orbit n =
2?
3. What is the energy of the electron in orbit n =
3?
4. In which orbit will the electron have the
highest energy, n=1, n=2, or n=3?

14. Exercises
5. As the value of n increases, what happens to
the energy value of the electron?

15.  E1 is the lowest energy and, the most stable
state. It is called the ground state or the
ground level. E2, E3, E4, etc. have higher
energies and are less stable than E1. They are
called excited states or excited levels.
 Note also that as the electron gets closer to the
nucleus, it becomes more stable.

16.  When energy is absorbed by the atom, the
electron gets excited and jumps from a lower
orbit to a higher orbit. When electrons go from
a higher energy level to a lower energy level,
it emits radiation. According to Bohr, if an
electron jumps from one orbit to another, it will
absorb or emit energy in quanta equal to:

18.  Bohr model explains the experimental emission
spectrum of hydrogen which includes a wide
range of wavelengths from the infrared to the
UV region.
Series n final n initial Spectrum Region
Lyman 1 2,3,4 ultraviolet
Balmer 2 3,4,5 visible & ultraviolet
Paschen 3 4,5,6 infrared
Brackett 4 5,6,7 infrared

19. Exercises
1. The electron in the hydrogen atom undergoes
a transition from n=3 to n=2.
a. Is energy absorbed or emitted?
b. What is the energy involved in the transition?
c. What is the wavelength (in nm)
corresponding to this transition?
d. What region of the electromagnetic spectrum
will this be?

20. Exercises
2. Which transition of the electron in the
hydrogen atom will involve the highest
frequency?
a. n = 5 to n = 3
b. n = 4 to n = 3
c. n = 5 to n = 2

21. THE LIMITATIONS OF THE BOHR
MODEL OF THE ATOM
a. It cannot explain the spectrum of atoms
with more than one electron.
b. It cannot explain the relative intensities of
spectral lines (why are some lines more
intense than others)
c. It cannot explain why some lines are slit
into several components in the presence
of a magnetic field (called the Zeeman
effect)

22. d. According to the Bohr model, when
electrons go around the nucleus in certain
orbits, its energy remains constant. But
moving electrons would lose energy by
emitting electromagnetic waves and the
electron is expected to spiral into the
nucleus.
e. It violates the Heisenberg’s Uncertainty
Principle. The Bohr model considers
electrons to have a known radius and orbit
which is impossible according to
Heisenberg.

23. THE DUAL NATURE OF THE ELECTRON:
DE BROGLIE’S EQUATION
 In 1924, Louis de Broglie made a bold proposition
based on Planck’s and Einstein’s concepts. De
Broglie reasoned that if light could have particle-
like properties, then particles like electrons
could also have wavelike properties.
 De Broglie’s idea – if the electron going around
the nucleus in a circular orbit behaves as a wave,
then it should behave as a standing wave. In a
standing wave, there are fixed points, or nodes,
where the amplitude is zero.

24.  De Broglie’s particle and wave properties is
given by the De Broglie equation:

25.  Where h is Planck’s constant, m is the mass of
the particle, and u is the velocity.
 Therefore, a particle in motion can be treated
as a wave and a wave can exhibit properties of
a particle.
 An electron has both particle and wavelike
properties – this is referred as the dual nature
of matter.

26. EXPERIMENTAL EVIDENCE OF
DE BROGLIE WAVELENGTH
 Waves associated with material particles were
called by de Broglie as “matter waves”. If
matter waves exist for small particles, then
beams of particles, such as electrons, should
exhibit the properties of waves, like
diffraction.

27.  Diffraction refers to various phenomena which
occur when a wave encounters an obstacle or a
slit.
 In classical physics, the diffraction
phenomenon is described as the interference
of waves. If the distance between objects that
the waves scatter from is about the same as the
wavelength of the radiation, diffraction occurs
and an interference pattern occurs.

28. Flame test
 One method of demonstrating the emission
spectrum of substances through a qualitative
analysis
 In this technique, a small amount of substance
is heated. The heat of the flame excites the
electrons of the metals ions, causing them to
emit visible light the color of which is unique
to the metal ion.

29. Flame colors
Metal ion Flame color
Li Red
Na Yellow
K Lilac
Ca Orange/Yellow-red
Sr Red
Ba Pale green
Cu Blue green