Expert answer:Hi, I am doing an experiment called Balmer Line of Hydrogen. I would like you to do the calculation and organize similar to the example that i have attached ” Balmer example file”. I have also made the graphs for each one of it. I just want you to do the calculation and submit the results similar to the example. Show me everything was written in the example.however, I want you to use my datas. the Zip file has the data for each on in case you need to graph them again and get the calculations. Good luck and follow what the Handout File is asking you for.
balmer_example_file.docx
balmer_line_datas.zip
balmer_graphs_.docx
handout_file.pdf
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DATA & RESULTS
Enlargement of Figure
3 is attached to the
back.
Figure 3. Mercury Spectrum Test.
The mercury was used to test the apparatus, to make sure the wavelength of the
mercury was correct and to calibrate the USB4000 as well as the HR4000.
Enlargement of Figure
4 is attached to the
back.
Figure 4. The Balmer line spectra for hydrogen.
λ (nm)
Wavenumber
n-2
ni
R (nm-1)
σR (nm-1)
410.16
0.00244
0.028
6
0.0109710 0.0000005
434.06
0.00230
0.040
5
0.0109710 0.0000005
486.10
0.00206
0.063
4
0.0109720 0.0000005
657.40
0.00152
0.111
3
0.0109520 0.0000003
Table 2. Wavelength and Calculated Rydberg’s Constant for Hydrogen Spectrum.
The following equation was used to find the uncertainty in R for the wavelengths of the
hydrogen spectrum from equation 1:
= √(
2
2
2
) ( ) + ( ) ( )2
(10)
Average Experimental R
0.0109665
(nm)
±0.00001
Corrected Experimental R
0.010969702
(nm)
±0.00001
Accepted R (nm)
0.0109678
% Difference
0.02
Table 3. Rydberg’s Average Experimental Constant.
The average of experimental R was corrected using the following equation, since the
experiment was not done in a vacuum3:
( ) = ( )
Where nair = 1.000292.
(11)
Figure 5. The relationship between Wavenumber and 1/N to find the Balmer series
limit.
Figure 6. The relationship of Wavenumber vs. 1/n-2.
The slope from figure 5 can also determine the Rydberg constant, which is 0.011 nm-1.
The percent difference from the accepted value, 0.0109697 nm-1 is 0.28%. Using the y-intercept
of the graph, the Balmer series limit can be determined:
1
1
=
∞ −
(12)
The y-intercept from the graph is 0.00274. After using equation 12 to calculate the Balmer
series limit, it is determined to be 365.0nm. The accepted Balmer series limit is 364.5nm. The
percent difference is 0.14%.
Ionization
potential
(eV)
3
1.511
4
0.85
5
0.544
6
0.378
Table 4. Potential Ionization of the Balmer Series.
(eV)
n
Figure 7. The relationship between Ionization potential and n.
Enlargement of Figure
8 is attached to the
back.
Figure 8. Hydrogen – Deuterium Mixture spectrum lines using USB4000.
The isotope shift for the hydrogen – deuterium mixture was predicted to be 0.17850nm,
using equation 7. The experimental peak for hydrogen was 656.295nm and the experimental
peak for deuterium was 656.119nm. The experimental isotope shift was determined to be
0.17608nm. The percent difference is 1.36%.
Enlargement of
Figure 9 is attached
to the back.
Figure 9. Zoomed in peak of Hydrogen Deuterium Mixture with USB4000.
In figures 8, we see the hydrogen-deuterium spectrum with several peaks. In figure 9, it
is observed that there is only one peak, where the shift is shown. When using the USB4000
spectroscopy, the hydrogen and deuterium peaks are not defined separately.
Enlargement of
Figure 10 is
attached to the
back.
Figure 10. Hydrogen – Deuterium Mixture spectrum lines using HR4000.
Enlargement of
Figure 11 is
attached to the
back.
Intensity (Counts)
Figure 11. Zoomed in peak of Hydrogen Deuterium Mixture with HR4000.
Wavelength (nm)
Figure 12. Cumulative Peak for Hydrogen- Deuterium Mixture using HR4000.
The isotope shift is shown in figures 11 and 12. The approximate shift is 0.18nm, by looking at
the distance of the peaks of the spectra of the mixture. The HR4000 show much more define
peaks for the hydrogen and deuterium, which is why two peaks are observed.
Using equation 7, the mass ration of hydrogen-deuterium can be calculated. The
expected value for the mass ratio (MD:MH) is 1.998. The experimental calculated ratio is 1.985.
The percent difference is 0.65%.6
The mass of an electron is then calculated using equation 8. The experimental electron
mass is 5.417 x 10-4 amu. The accepted electron mass value is 5.485 x 10-4 amu. The percent
difference is 1.27%.3
HR4000 Mix
2D Graph 2
14000
12000
10000
Y Data
8000
6000
4000
2000
0
-2000
560
580
600
620
640
X Data
Col 1 vs Col 2
660
680
700
HR4000-H graph
14000
12000
10000
1/n^2
8000
6000
4000
2000
0
-2000
560
580
600
620
640
wave
Col 1 vs Col 2
660
680
700
HR4000-H graph
14000
12000
10000
1/n^2
8000
6000
4000
2000
0
-2000
560
580
600
620
640
wave
Col 1 vs Col 2
Col 1 vs Col 2
660
680
700
H- graph
70000
60000
50000
1/n^2
40000
30000
20000
10000
0
-10000
300
400
500
600
700
wave (nm)
Col 1 vs Col 2
800
900
1000
1100
Hg graph
70000
60000
50000
1/n^2
40000
30000
20000
10000
0
-10000
300
400
500
600
700
wave (nm)
Col 1 vs Col 2
800
900
1000
1100
The Balmer Lines of Hydrogen
Purpose: To measure and interpret the Balmer line spectra series of hydrogen and determine the mass of
Deuterium atom.
Apparatus:
1. Ocean Optics USB4000 & HR 4000 Fiber
Optics Spectrometers
2. PC
3. Hydrogen/Deuterium spectrum tube
4. Mercury spectrum tube
5. Hydrogen Spectrum Tube
Introduction:
In 1885 Johann Balmer (a Swiss schoolteacher), succeeded in obtaining a simple relationship among
the wavelengths of the lines in the visible region of the hydrogen spectra:
2
= 2n
(1)
where n = 3, 4, 5, . . .; n > 2
n -4
where λ = 364.25 nm is a constant which the series approaches as n -> . It is more convenient to
express them in terms of wave number (1/λ)
1
1
1
= = R 2 – 2
2 n
where n = 3, 4, 5, . . .; n > 2
(2)
where R is the Rydberg constant for hydrogen and . Twenty-three years later, other series of the hydrogen
atom’s spectral lines were discovered. By 1924 five series had been discovered, and they are
Hydrogen Series of Spectral Lines
Discoverer (year)
Wavelength
nf
ni
Lyman (1916)
Ultraviolet
1
>1
Balmer (1885)
Visible, ultraviolet
2
>2
Paschen (1908)
Infrared
3
>3
Brackett (1922)
Infrared
4
>4
Pfund (1924)
Infrared
5
>5
Bohr theory of hydrogen atom, as well as quantum mechanics gives for the hydrogen lines,
1 1
= R 2 – 2
n f ni
1
where R =
2 2 me4
= 1.09737309 x 107 m-1
2
3
c h (4 0 )
(4)
where m and e are the mass and charge of the electron, c is the velocity of light, h is Planck’s constant, and
nf and ni are integers with nf < ni.
The Bohr formula given above was derived assuming that the nucleus had infinite mass and does not
move as the electron "orbits" about it. Taking into account that the electron and proton move about the
center of mass, we replace the mass m of the electron by the reduced mass μ of the atomic system:
=
m
m
1+
MH
(5)
where MH is the hydrogen nuclear mass. This value for the Rydberg constant agrees extremely well with
experiment and is given by
RH =
MH
7
-1
R = 1.09677576 10 m
MH +m
(6)
It was discovered that many spectral lines possess an aggregate of very fine lines which could not explained
This can be explained with existing theory based on electronic structure of the atom. Systematic studies
reveled that there are two kinds of hyperfine structure. One kind arises from the presence of several
isotopic nuclei for a given chemical element and this is known as isotope shift. For light atoms such as
hydrogen, the isotope shift appears to arise from simple differences in the effects of nuclear motion. For
heavy atom, the isotope shifts are found, in general, to be proportional to the differences in atomic mass.
The second kind of hyperfine shift was first explained by Pauli in 1924 as due to the fact that nucleus
possess an angular momentum and an associated magnetic moment and it interacts with the outer electrons.
We are only interested in the isotope shift. In the case of hydrogen, the isotope shift was used as a
guide by Urey and his collaborators in the discovery of heavy hydrogen H2 or deuterium, D. The Rydberg
constant for deuterium is given by
RD =
MD
R
MD+m
where MD is the deuterium mass.
H-D Spectra
2
(7)
Apparatus: Learn about USB4000 and HR 4000 Fiber Optics Spectrometers from Installation and
Operation Manuals (Manuals are at your work station and on the BB site). The schematics and
principle of operation of the spectrometers should be included in your lab report.
The Geissler atomic hydrogen gas discharge tube has an atmosphere of pure water vapor which
dissociates into hydrogen ions and atoms. The H2 molecules which are also formed during the discharge
are continuously purged from the lamp and converted to water vapor by a special cartridge inside the
electrodes. You will also use a special Geissler tube containing 50 % hydrogen and 50 % deuterium. The
other apparatus used includes a mercury discharge tube, associated electronics and computer.
UV LIGHT WARNING
DO NOT STARE AT THE MERCURY OR HYDROGEN LIGHT!
A. Determining the Wavelengths of Balmer Series (USB4000 Spectrometer)
Before you begin, check the calibration coefficients of the USB400 spectrometer to make sure
that these have the factory set values. If the values are different, please contact the instructor
before beginning
1. Run the Ocean View software. Familiarize yourself with its operation. [Refer to the manual and
understand the controls and settings. You will collect data in the QuickView mode].
2. Set up a hydrogen tube. Record its spectrum using the USB 4000 spectrometer. Also, record the
spectra of the Deuterium tube and the Hydrogen-Deuterium mix. Examine if there are any differences.
[Steps 2 through 7 need to be carried out only for the hydrogen spectrum].
2. Determine the wavelength of all the lines observed in the wavelength region from 380nm to 660nm.
Compare your results with the accepted values listed in Handbook of chemistry and Physics.
3. Use Equation 2 to determine the Rydberg RH for each of the lines of the Balmer series. Take an
average of your RH (air) values, and correct it to vacuum using the index of refraction of air (nair =
1.000292):
(8)
RH (vacuum)= nair RH (air)
4. Also plot the wave number versus n-2. From the slope determine the Rydberg constant. Compare wuth
H-D Spectra
3
accepted value.
5. Calculate the Ionization Potential of hydrogen atom using your Ryderg constant value. Compare with
the accepted value.
6. From the y-intercept determine the Balmer series limit.
7. Compare the calculated values with the accepted values.
B. Calibration of USB 4000 Spectrometer using the Mercury-Argon source [ Important: do not
calibrate the HR 4000 spectrometer].
1. Set up the Mercury- Argon source and position the optical fiber for light collection and measurement
using the USB4000 spectrometer. Note that there is a special optical fiber to be used for calibration.
3. Familiarize yourself with the calibration method and steps
4. Record the Mercury-Argon spectrum after optimizing the parameters
5. Record the spectrum of the pure Mercury source. Tabulate and compare the observed values and listed
values in the CRC handbook. Estimate the error %
6. Record the spectrum of the hydrogen source. Tabulate and compare the observed values and listed
values in the CRC handbook. Estimate the error %.
7. Record the spectrum of the Hydrogen-Deuterium source.
6.
Calibrate the spectrometer using the listed values of spectral lines. Be sure to save your calibration
coefficients and report these.
7.
Repeat steps 5 and 6. Compare the Mercury and Hydrogen spectra before and after Calibration.
Explain any differences or lack thereof.
[The calibration procedure and results must be discussed in your report. Comment on any differences
you observe between the two spectrometers including possible reasons].
8. Restore the calibration coefficients to factory-set values.
C. Mass of Deuterium Atom. [ You will use HR 4000 for this experiment].
1. Remove the hydrogen tube and replace it with the Deuterium tube. Record its spectrum. To
compare H spectrum and D spectrum, they should be plotted on the same graph (lines should have
H-D Spectra
4
similar intensities). To determine the exact position of the lines, you should zoom on each line
separately and include these data in your report. Do you observe the shift of the lines?
2. Repeat (1) with the tube containing Hydrogen-Deuterium mixture.
3. Compare results in (2) with spectra you obtained for Hydrogen-Deuterium mix with USB 4000.
Explain any differences or lack thereof using your information on how the two spectrometers differ.
3. For any given line of the series, the isotope shift (λH. - λD) may be written as
MD -1
H - D = M H
M D +1
D
m
(9)
where m, MH, MD are the masses of the electron, proton, and deuteron, respectively. From your data
compute MD / MH, the ratio of Deuterium/Hydrogen masses. Compare with the expected value. Do this
for both (1) and (2).
[ Equation-9 must be derived in the theory section of your report].
3. Show that if the atomic masses of H and D are known, then the mass of the electron is given by
m= M H M D
D - H
M D H - M H D
(10)
where v are wave numbers (1/λ). From your data and known values of MD and MH compute the mass
of the electron. Compare with the accepted value.
H-D Spectra
5
...
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