Atomic Emission Spectra of Hydrogen
Thomas Ehret
Adam Cooke, Marc Hnatyshin
B.C. Boivin
SPH4U, Grade 12 University Physics, Rockland District High School
Friday, April 19th, 2013.
Introduction:
The goal of this lab is to accurately measure the energy of various light waves for the
atomic emission spectra of Hydrogen.
The Electromagnetic Spectrum is a scale that shows the correlation between
wavelength and frequency of all
waves with electromagnetic radiation
(See Figure 1.). When the wavelength
of the electromagnetic radiation
waves is larger, the frequency is
lower, and when the wavelength is
smaller, the frequency is higher. The
radiation of the waves with higher
frequencies like Gamma Rays and XFigure 1. The Electromagnetic Spectrum
Rays tend to be the most harmful. The demonstrating wavelengths and frequencies
(Anonymous, 2012).
Visible Spectrum portion of the
Electromagnetic Spectrum is the only
part of the scale that the human eye can witness.
The Atomic Emission
Spectra describes the specific
frequencies emitted by an atom
when it is subject to having energy
inputted into it. This was
discovered because it was found
Figure 3.
2. The Atomic Emission Spectra of Hydrogen.
Colours shown from the four distinct frequencies given
off (Anonymous, How Our Body Might Collect
Information, 2011).
that orbits become quantized and
allow electrons to jump from orbit
to orbit. When the orbit they jump
to has more energy than the
original, the electron absorbs a photon with a specific frequency, but when it jumps to an orbit
with less energy, the electron gives off a photon with a specific frequency (Anonymous, atomic
spectrum, 2005). A photon is described to be a quanta of light or in simpler terms, a particle. It
is a packet of energy that
moves in the form of a wave
which makes light unique
towards other waves
(Anonymous, Photons As
Light Quanta). The specific
frequencies that these
photons are giving off differ
for different types of atoms
and elements. For example, a
Figure 4. Planck’s constant shown in an example where an
electron is jumping to another orbit (Norton, 2013).
Hydrogen atom will normally
give off frequencies that demonstrate the colours red (𝜆 = 656.2nm), teal (𝜆 = 486.1nm), indigo
(𝜆 = 434nm), and violet (𝜆 = 410.1nm) that each, as shown, have their own specific wavelength
as well (Anonymous, Emission Spectrum of Hydrogen). These colours are in the order that you
would see them on the electromagnetic spectrum (See Figure 2.).
Niels Bohr was one of the scientists that discovered and theorized about what was
happening when electrons jump from orbit to orbit (See beginning of second paragraph). One
of which was that there are certain orbits in atoms where the electrons do not emit energy.
Another was that when there is an emission or absorption of radiation, it means that an
electron is jumping from one orbit to another (Students). Max Planck was a theoretical physicist
who helped develop the quantum theory. He discovered that action did not take on any value
for different situations. Planck then came up with the constant, ‘quantum of action’ which is
now called Planck’s constant. This constant appears in equations used in physics such as: Δ𝐸 =
ℎ𝑓, where ‘h’ is the symbol used for the constant (See Figure 3.).
The purpose of this experiment was to experimentally determine the energy of each
light wave of the atomic emission spectra of Hydrogen by reenacting Bohr’s lab Rockland style.
Theory:
𝑐 = 𝜆𝑓
𝑐 - speed of wave, or speed of light (usually speed of light)
𝜆 - wavelength of the wave
𝑓 - frequency of the wave
Δ𝐸 = ℎ𝑓
Δ𝐸 - Change in energy of the wave
ℎ - Planck’s constant, quantum of action (Anonymous, Planck constant, 2013).
𝑓 - frequency of the wave
%𝐸𝑟𝑟𝑜𝑟 =
|𝐸𝑚𝑝𝑖𝑟𝑖𝑐𝑎𝑙 − 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙|
𝑥 100%
𝐸𝑚𝑝𝑖𝑟𝑖𝑐𝑎𝑙
Materials and Methods:
The
materials and
methods used in
this experiment
were those of the
class, SPH4U on
Thursday, April
11th, 2013.
Figure 5. Atomic Emission Spectra of Hydrogen lab setup. Asif Nazerally
looking through a spectroscope into the hydrogen light source
(Hendrix-Sicard).
Results and Observations:
Table 1. Atomic Emission Spectra for 𝐻2 . Experimental values.
Spectral Line Colour
𝒇 (Hz)
𝝀 (nm)
Red
Teal (Blue-Green)
Indigo (Blue-Violet)
Violet
700
500
475
450
14
4.29 𝑥 10
6 𝑥 1014
6.32 𝑥 1014
6.67 𝑥 1014
𝜟𝑬 (J)
2.84 𝑥 10−19
3.98 𝑥 10−19
4.19 𝑥 10−19
4.42 𝑥 10−19
Table 2. Atomic Emission Spectra for 𝐻2 . Empirical values.
Spectral Line Colour
𝒇 (Hz)
𝝀 (nm)
Red
Teal (Blue-Green)
Indigo (Blue-Violet)
Violet
656.2
486.1
434
410.1
Calculations:
Red (experimental):
𝑐
𝑓=
𝜆
𝑐 = 3 𝑥 108 𝑚/𝑠
3 𝑥 108 𝑚/𝑠
𝑓=
700 𝑥 10−9 𝑚
𝑓 = 4.29 𝑥 1014 𝐻𝑧
Δ𝐸 = ℎ𝑓
ℎ = 6.63 𝑥 10−34 𝐽 𝑥 𝑠
Δ𝐸 = (6.63 𝑥 10−34 𝐽 𝑥 𝑠)(4.29 𝑥 1014 𝐻𝑧)
Δ𝐸 = 2.84 𝑥 10−19 𝐽
Red (empirical):
𝑐
𝑓=
𝜆
3 𝑥 108 𝑚/𝑠
𝑓=
656.2 𝑥 10−9 𝑚
𝑓 = 4.57 𝑥 1014 𝐻𝑧
Δ𝐸 = ℎ𝑓
Δ𝐸 = (6.63 𝑥 10−34 𝐽 𝑥 𝑠)(4.57 𝑥 1014 𝐻𝑧)
14
4.57 𝑥 10
6.17 𝑥 1014
6.91 𝑥 1014
7.32 𝑥 1014
𝜟𝑬 (J)
3.03 𝑥 10−19
4.09 𝑥 10−19
4.58 𝑥 10−19
4.85 𝑥 10−19
Δ𝐸 = 3.03 𝑥 10−19 𝐽
Red (Percentage of error):
%𝐸𝑟𝑟𝑜𝑟 =
|𝐸𝑚𝑝𝑖𝑟𝑖𝑐𝑎𝑙 − 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙|
𝑥 100%
𝐸𝑚𝑝𝑖𝑟𝑖𝑐𝑎𝑙
|3.03 𝑥 10−19 − 2.84 𝑥 10−19 |
%𝐸𝑟𝑟𝑜𝑟 =
𝑥 100%
3.03 𝑥 10−19
%𝐸𝑟𝑟𝑜𝑟 = 6.27%
Teal (experimental):
𝑐
𝑓=
𝜆
𝑐 = 3 𝑥 108 𝑚/𝑠
𝑓=
3 𝑥 108 𝑚/𝑠
500 𝑥 10−9 𝑚
𝑓 = 6.00 𝑥 1014 𝐻𝑧
Δ𝐸 = ℎ𝑓
ℎ = 6.63 𝑥 10−34 𝐽 𝑥 𝑠
Δ𝐸 = (6.63 𝑥 10−34 𝐽 𝑥 𝑠)(6.00 𝑥 1014 𝐻𝑧)
Δ𝐸 = 3.98 𝑥 10−19 𝐽
Teal (empirical):
𝑐
𝑓=
𝜆
𝑓=
3 𝑥 108 𝑚/𝑠
486.1 𝑥 10−9 𝑚
𝑓 = 6.17 𝑥 1014 𝐻𝑧
Δ𝐸 = ℎ𝑓
Δ𝐸 = (6.63 𝑥 10−34 𝐽 𝑥 𝑠)(4.57 𝑥 1014 𝐻𝑧)
Δ𝐸 = 4.09 𝑥 10−19 𝐽
Teal (Percentage of error):
%𝐸𝑟𝑟𝑜𝑟 =
|𝐸𝑚𝑝𝑖𝑟𝑖𝑐𝑎𝑙 − 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙|
𝑥 100%
𝐸𝑚𝑝𝑖𝑟𝑖𝑐𝑎𝑙
|4.09 𝑥 10−19 − 3.98 𝑥 10−19 |
%𝐸𝑟𝑟𝑜𝑟 =
𝑥 100%
4.09 𝑥 10−19
%𝐸𝑟𝑟𝑜𝑟 = 2.69%
Indigo (experimental):
𝑐
𝑓=
𝜆
𝑐 = 3 𝑥 108 𝑚/𝑠
𝑓=
3 𝑥 108 𝑚/𝑠
475 𝑥 10−9 𝑚
𝑓 = 6.32 𝑥 1014 𝐻𝑧
Δ𝐸 = ℎ𝑓
ℎ = 6.63 𝑥 10−34 𝐽 𝑥 𝑠
Δ𝐸 = (6.63 𝑥 10−34 𝐽 𝑥 𝑠)(6.32 𝑥 1014 𝐻𝑧)
Δ𝐸 = 4.19 𝑥 10−19 𝐽
Indigo (empirical):
𝑓=
𝑐
𝜆
3 𝑥 108 𝑚/𝑠
𝑓=
434 𝑥 10−9 𝑚
𝑓 = 6.91 𝑥 1014 𝐻𝑧
Δ𝐸 = ℎ𝑓
Δ𝐸 = (6.63 𝑥 10−34 𝐽 𝑥 𝑠)(6.91 𝑥 1014 𝐻𝑧)
Δ𝐸 = 4.58 𝑥 10−19 𝐽
Indigo (Percentage of error):
%𝐸𝑟𝑟𝑜𝑟 =
|𝐸𝑚𝑝𝑖𝑟𝑖𝑐𝑎𝑙 − 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙|
𝑥 100%
𝐸𝑚𝑝𝑖𝑟𝑖𝑐𝑎𝑙
%𝐸𝑟𝑟𝑜𝑟 =
|4.58 𝑥 10−19 − 4.19 𝑥 10−19 |
𝑥 100%
4.58 𝑥 10−19
%𝐸𝑟𝑟𝑜𝑟 = 8.52%
Violet (experimental):
𝑐
𝑓=
𝜆
𝑐 = 3 𝑥 108 𝑚/𝑠
𝑓=
3 𝑥 108 𝑚/𝑠
450 𝑥 10−9 𝑚
𝑓 = 6.67 𝑥 1014 𝐻𝑧
Δ𝐸 = ℎ𝑓
ℎ = 6.63 𝑥 10−34 𝐽 𝑥 𝑠
Δ𝐸 = (6.63 𝑥 10−34 𝐽 𝑥 𝑠)(6.67 𝑥 1014 𝐻𝑧)
Δ𝐸 = 4.42 𝑥 10−19 𝐽
Violet (empirical):
𝑐
𝑓=
𝜆
3 𝑥 108 𝑚/𝑠
𝑓=
410.1 𝑥 10−9 𝑚
𝑓 = 7.32 𝑥 1014 𝐻𝑧
Δ𝐸 = ℎ𝑓
Δ𝐸 = (6.63 𝑥 10−34 𝐽 𝑥 𝑠)(7.32 𝑥 1014 𝐻𝑧)
Δ𝐸 = 4.85 𝑥 10−19 𝐽
Violet (Percentage of error):
%𝐸𝑟𝑟𝑜𝑟 =
|𝐸𝑚𝑝𝑖𝑟𝑖𝑐𝑎𝑙 − 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙|
𝑥 100%
𝐸𝑚𝑝𝑖𝑟𝑖𝑐𝑎𝑙
%𝐸𝑟𝑟𝑜𝑟 =
|4.85 𝑥 10−19 − 4.42 𝑥 10−19 |
𝑥 100%
4.85 𝑥 10−19
%𝐸𝑟𝑟𝑜𝑟 = 8.87%
Discussion:
In this experiment, the students used a spectroscope to look at a Hydrogen discharge
tube to see the atomic emission spectra of Hydrogen. The atomic emission spectra of Hydrogen
will show the colours red, teal, indigo, and violet, and has a set of empirical values for the
colours` wavelength, frequency, and energy. The goal was to experimentally get values that
were close to the empirical values. The percentage of errors calculated in order by red, teal,
indigo, and violet were 6.27%, 2.69%, 8.52%, and 8.87%. All these values are less than 10%
which would make it considerably a successful experiment.
There are a few possible sources of error that could have skewed the results to make
them unequal to the empirical values. One could be that there was too much light in the room
when conducting the experiment. Ideally when doing experiments where there is light involved,
having a room with very little light is better. The light can degrade the light coming from the
discharge tube and generally give you inaccurate results. This could have been fixed by planning
the experiment earlier and using the classroom that does not have any windows. Another
possible source of error is that the Hydrogen discharge tube being used for the experiment was
not pure, meaning that it was not pure Hydrogen emitting the light. Another gas such as Argon
or Neon could have been helping with the emission of the light. This would skew the results by
giving the wrong colour input into the spectroscope which would give us a skewed wavelength
value. This could only be fixed by somehow purifying the discharge tube or buying a new
discharge tube that was purely Hydrogen. A third possible source of error could be that the
spectroscopes that were used are old and not completely functional. This could skew the
results by again, giving a slightly different value for the wavelength causing all your calculations
to be off. The only solution for this would be to buy new, perfectly functional spectroscopes.
Conclusion:
It was experimentally determined that the energy for red was 2.84 𝑥 10−19 𝐽 with a
percentage of error of 6.27%, for teal was 3.98 𝑥 10−19 𝐽 with a percentage of error of 2.69%,
for indigo was 4.19 𝑥 10−19 𝐽 with a percentage of error of 8.52%, and for violet was
4.42 𝑥 10−19 𝐽 with a percentage of error of 8.87%.
Selected References:
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http://www.thefreedictionary.com/Atomic+emission+spectrum
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http://drchemical.com.au/category/uncategorized/page/2
Anonymous. (n.d.). Emission Spectrum of Hydrogen. Retrieved April 18, 2013, from Chem-Ed:
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch6/bohr.html
Anonymous. (2011, January 26). How Our Body Might Collect Information. Retrieved April 16,
2013, from Touchy Subjects: http://touchysubjects.wordpress.com/2011/01/26/how-our-bodymight-collect-information/
Anonymous. (n.d.). Photons As Light Quanta. Retrieved April 18, 2013, from Michigan State
University Physics 232:
http://www.pa.msu.edu/~pratts/phy232/lectures/quantum/photons.html
Anonymous. (2013, April 4). Planck constant. Retrieved April 17, 2013, from Wikipedia:
https://en.wikipedia.org/wiki/Planck_constant
Hendrix-Sicard, M. Lab setup . Rockland.
Norton, J. D. (2013, April 6). Origins of Quantum Thoery. Retrieved April 18, 2013, from Pitt
Education:
http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/quantum_theory_origins/
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