HW 4 Solutions (PDF)

CHEM 155 Instrumental Analysis Prof. Terrill DH-007 924-4970 rterrill@jupiter.sjsu.edu Page 1 of 4 

Homework Assignments for the Semester 


HW-4. Answer the following questions: 

4.1. Why do gas phase atoms 

exhibit UV-Visible line spectra 

whereas molecules exhibit 

band spectra 

Firstly, gas phase atoms do not have 

vibrational fine structure (only molecules 

vibrate – vibration meaning oscillatory 

motion of the nuclei in the molecule), so 

only the electronic energy levels are seen 

in the UV-Visible spectra. Secondly, the 

electronic energy levels are nearly 

perfectly unperturbed by neighboring 

atoms, so each atoms absorbs or emits 

at exactly the same wavelength – i.e. 

there is virtually no broadening of the 

spectral lines. 

Energy / eV 

5 

4 

3 

2 

1 

4.2. Using the diagram to the right, 

predict approximately a. the 

absorbance spectrum b. the fluorescence emission spectrum (assume 

excitation at about 250nm) and c. the infrared absorbance spectrum of 

this molecule. Label the x-axis in nm for parts a and b, and in 

wavenumbers (cm -1 ) for part c. Of course there is no way to predict 

band intensities based on this information, just band positions. A 

hand sketch is fine, but a well-labelled wavelength / wavenumber axis 

is needed. Assume that the molecule is in the gas phase, so that the 

vibrational structure within the electronic transitions is resolvable for 

the larger vibrational transitions. 

See Below 

C:\SJSU\Teaching\155\2004 ASpring\Homework\2000 Fall Homework\Solutions\HW4 solutions.doc Page 1 of 4



This one required a little bit of graph reading. I measured the energy levels in 

mm, and then converted to eV using 5.0 eV = 61 mm. 

Next I just did straightforward energy calculations: ν = E/h, then λ = c/ν, then ν- 

bar = 1/λ(cm). This was convenient using Excel – but wouldn’t take much longer 

using a calculator! 

The absorbance spectrum appears between S 0 0 and S n 1 where n is the 

vibrational sublevel and varies between 0 and 6. 

The fluorescence spectrum has two branches: one from S 0 1 - S n o and one from 

T 0 1 - S n o . 

The infrared spectrum appears between S 0 0 and S n 0 . 

Number of mm that I measured… 

n 

n S o 

n n 

S 1 T o 

_______________________ 

0 0 45 34 

1 8 53 

2 12 57 

3 15 60 

4 17 61 

5 18 62 

6 19 63 

Number of millimeters of energy level on graph: 

n 

n 

n 

n S o S 1 T o 

0 0 45 34 

1 8 53 - 

2 12 57 - 

3 15 60 - 

4 17 61 - 

5 18 62 - 

6 19 63 - 

Energy in electron volts = #mm * 5.0/6.1 

n 

n 

S o 

n 

S 1 n 

T 1 S 0 n 

1 - S o T 0 n 

1 - S o 

0 0.00 3.69 2.79 3.69 2.79 

1 0.66 4.34 - 3.03 2.13 

2 0.98 4.67 - 2.70 1.80 

3 1.23 4.92 - 2.46 1.56 

4 1.39 5.00 - 2.30 1.39 

5 1.48 5.08 - 2.21 1.31 

6 1.56 5.16 - 2.13 1.23 




Frequency in Hz v = E/h 

n 

n 

S o 

n 

S 1 n 

T 1 S 0 n 

1 - S o T 0 n 

1 - S o 

0 0.00E+00 8.92E+14 6.74E+14 8.92E+14 6.74E+14 

1 1.59E+14 1.05E+15 - 7.33E+14 5.15E+14 

2 2.38E+14 1.13E+15 - 6.54E+14 4.36E+14 

3 2.97E+14 1.19E+15 - 5.95E+14 3.77E+14 

4 3.37E+14 1.21E+15 - 5.55E+14 3.37E+14 

5 3.57E+14 1.23E+15 - 5.35E+14 3.17E+14 

6 3.77E+14 1.25E+15 - 5.15E+14 2.97E+14 

Wavelength in nm = L = c/v 

n 

S o 

n 

S 1 

n 

n 

T 1 S 0 n 

1 - S o T 0 n 

1 - S o 

0 - 336 445 336 445 

1 1892 286 - 409 582 

2 1262 266 - 459 688 

3 1009 252 - 505 797 

4 890 248 - 541 890 

5 841 244 - 561 946 

6 797 240 - 582 1009 

Wavenumber in cm-1 = 1E7/ L 

n 

n 

S o 

n 

S 1 n 

T 1 

0 - 29726 22460 

1 5285 35011 - 1 

2 7927 37653 - 1 

3 9909 39635 - 1 

4 11230 40296 - 1 

5 11891 40956 - 1 

6 12551 41617 - 1 




Absorbance and Fluorescence Lines 

0.9 

0.8 

0.7 

Intensity / Arbitrary Units 

0.6 

0.5 

0.4 

0.3 

0.2 

S1-S0 Fluroescence vs Lambda 

/ nm 

T10-S0n Phosphorescence 

Absorbance lines S0-S1n 

0.1 

0 

200 400 600 800 1000 

Lambda / nm 

Infrared Absorbance - S00-S0n 

1.2 

Absorbance / arbitrary units 

1 

0.8 

0.6 

0.4 

0.2 

0 

4000 6000 8000 10000 12000 14000 

Wavenumber / cm-1

HW 4 Solutions (PDF)

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