Lab Atomic Emission Spectra PDF

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Lab report on atomic emission spectra...

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Atomic Emission Spectra Experiment #7

Teacher: Jaleel Ali

Lab section: 19 & 20 202-NYA-05

Thursday, November 2nd, 2017

I. introduction In this experiment, a spectroscope was used. This instrument splits light into the different wavelengths that it is made of 1. The objective of this experiment was to determine the wavelengths of the spectral lines of hydrogen by utilizing the calibration of the spectroscope when observing helium. A calibration curve was done using the values gotten from the observation of helium. Bohr’s model of hydrogen was based on the assumption that electrons moved in specific orbits. In addition, the equation that helped him calculate the energy of an electron in a specific shell −B where B is a constant and its value is 2.178 x 10-18 was the following: E= 2 n J. In order to explain the hydrogen spectrum, he used the concept of electrons absorbing and emitting photons when moving from one orbit to another. The photon energy associated to this is:

(

E photon = E out−E¿ =B

1 2 ¿

n

−

1 2

nout

)

Figure 2 in the laboratory manual showed the energy level diagram for hydrogen. This was used in order to validate the results. Unfortunately, Bohr’s model did not apply for systems containing more than one electron. Physicists Max Planck and Albert Einstein formed the theory that electromagnetic radiation had the behavior of waves and photons. It was Planck who proposed that emitted electromagnetic radiation was quantized. In other words, it could only have values associated hc to the following equation2: E photon=hv = λ

II. Procedure Refer to the Laboratory Manual.

Iii. Data and Results Table 1: Helium Emission Spectrum Colour Relative Intensity

Wavelength (nm)

Scale reading

red

70

706.5

0.70

red

100

667.8

1.20

yellow

1000

587.6

2.65

light green

15

504.8

5.05

light green

100

501.6

5.25

dark green

50

492.2

5.60

blue

40

471.3

6.65

blue-violet

100

447.1

7.85

violet

30

438.8

8.30

violet

25

412.1

10.35

violet

70

402.6

11.15

violet

50

396.4

12.60

Table 2: Hydrogen Emission Spectrum Colour

Spectroscope Scale

Wavelength nm (from calibration curve)

Wavelength nm (from Fig 2)

red

1.40

645

656.3

green blue

5.90

484

486.1

violet

7.00

467

434.1

violet

8.70

447

410.2

Table 3: Comparison with Bohr Theory Colour

% error in wavelength

nout

nin

Rydberg’s constant, m-1 (from experimental λ )

red

-1.75

3

2

1.12 x 107

green blue

-0.513

4

2

1.10 x 107

violet

7.66

5

2

1.02 x 107

violet

9.08

6

2

1.01 x 107

Table 4: Average Rydberg Constant and % Error Average Rydberg Constant, m-1 % error

1.06 x 107 -3.31

Figure 1: Calibration Curve of Wavelength vs Scale Reading for Helium 800

f(x) = 689.79 x^-0.21 700

wavelength (nm)

600

500

400

300

200

100

0 0

2

4

6

8

scale reading

IV. Sample calculations 1) Wavelength of red (hydrogen) y=689.7 x−0.20 −0.20 y=689.7 ∙ 1.40 y=¿ 645 nm

10

12

14

2) % Error Wavelength experimental value−theoretical value ∙ 100 % error= theoretical value 645nm−656.3 % error= ∙100 656.3 % error=−1.75 %

3)

[

1 1 1 =R H 2 − 2 λ n¿ nout

[

] ]

1 1 1 =R H 2 − 2 −7 6.45 x 10 m 2 3 R H =¿ 1.12 x 107 4) Average Rydberg Constant 7

7

7

1.12 x 10 +1.10 x 10 +1.02 x 10 +1.01 x 10 4 7 -1 Average Rydberg Constant=¿ 1.06 x 10 m

Average Rydberg Constant=

5) % Error Rydberg Constant experimental value−t h eoretical value % error= ∙ 100 t h eoretical value 1.06 x 107 m−1−1.09737 x 107 m−1 ∙100 % error= 1.09737 x 107 m−1 % error=−3.31 %

7

V. Conclusion The average Rydberg constant was 1.06 x 107 m-1 and the percent error in wavelength was -1.75% for red, -0.513% for green blue, 7.66% for the first violet and 9.08% for the second violet. The purpose of this experiment was to determine the wavelengths of the spectral lines of hydrogen by utilizing the calibration of the spectroscope when observing helium. The objective was accomplished because the values of the wavelengths were found. In fact, it was accomplished to a high degree because the percent errors associated to the wavelengths were low. Even the percent error for the Rydberg Constant was little (-3.31%). Since the results were close to the actual values, they agreed with the theory. The calibration curve also gave what was expected, which was a curve with values close to the trend line. There a few possible sources of error that could have had an impact on the values. For example, some of the spectrum lines were harder to see. The relative intensities that were less than 50 were quite difficult to read because they were really faint. Therefore, there is a big probability that the values of the scale reading are not accurate for violet. Furthermore, some of the spectrum lines were thicker than others. Therefore, the specific point where it fell was subject to interpretation. Parallax could have also had an effect (2 different images).

vi. References 1

General Chemistry 202-NYA-05: Laboratory Experiments. Fall Semester, 2017. Chemistry Dept. Dawson College 2 ”Bohr’s Model of Hydrogen.”Khan Academy. N. p. n. d. Web. 12 Nov. 2017

vii. Answers to questions Pre-Laboratory Questions 1. In a normal hydrogen atom, when the electron occupies its lowest available energy state, the atom is said to be in its ground state. The maximum potential energy that an atom can have is 0 J, at which point the electron has essentially been removed from the nucleus; thus the atom is ionized. a) How much energy will it take to ionize a hydrogen atom in its ground state? En =

−B n2

En =

−2.178 x 10−18 J 1 −18

En=−2.178 x 10

J

b) Calculate the wavelength of light that would be required to effect this ionization?

E=

h∙c λ −18

2.178 x 10

=

6.626 x 10

−34

8

∙ 2.998 x 10

λ

λ=9.121 x 10−8 m c) Identify the series of spectral lines to which this wavelength belongs. −8

λ=9.121 x 10 m=91.21 nm Thus, the series of spectral lines is UV rays.

Post-Lab Questions 1. What is the identity of a hydrogen-like cation that has the following energy levels? ∆ E=−B Z 2

(

1 2 f

n

−

1 2

ni

) (21 − 11 )

−18 2 2.6138 x 10-17= −2.178 x 10 ∙ Z

2

2

Therefore, the cation is Be2+. 4=Z

2. Refer to the diagram below. a) Complete the diagram below to show all possible transitions when electrons go from n=5 state to the n=2 state.

n=5

n=4

n=3

n=2

b) Based on the number of transitions, which transition leads to the most intense line in the line spectrum? n=5 to n=4 and n=3 to n=2

3. The Li2+ ion has a ground state electron energy of -1.960 ∙ 10-17 J.

a) Determine the energy, in units of kJ/mol, required to raise 1.00 mol of Li 2+ ions each from their ground state to a final state of n=3. 1) 6.023 x 1023 1

Li2 +¿ions x

Li2+¿ion =¿ −17 −1.960 x 10 J ¿ 7

x=−1.180 x 10 J

2) ∆ E=−1.180 x 10

7

(

1 1 − 2 3 12

)

7

∆ E =1.049 x 10 J 4 ∆ E=1.049 x 10 kJ /mol

b) Calculate the wavelength of the light that would be required to ionize the Li 2+ ions if it is initially in its ground state E= 1.960 x 10−17=

hc λ

6.626 x 10−34 ∙ 2.998 x 108 λ

λ=¿ 10.14 nm 4. In the first part of this experiment a helium lamp is used to generate a calibration curve for scale reading vs wavelength. a) Why is a helium lamp used instead of a more traditional light source such as a standard tungsten filament light bulb? A helium lamp is used because there are not a lot of spectral lines. They are distinct and correspond to the ones of the gas studied. Contrary to the helium, the tungsten filament light bulb produces a continuous spectrum with all the visible colors and infrared. Therefore, it would be much harder to record the values for helium and then do a calibration curve.

b) Would a white light source such as sunlight also be appropriate? Justify your answer. A white light would not be appropriate because it contains all the colors. Since there is no pure substance, it would not be possible to recognize the lines corresponding to the helium. In order to be able to do the scale reading of a gas, the lamp has to be the same as the gas....