CM4002 Photochemistry and Lasers

Year’s Work on Laser section of module.

Answers:

1) What are the 4 energy levels involved in the operation of a diode laser?

This was not a simple question – the description of the behaviour of a diode laser is much more complicated than any of the other systems. Also I did not realize that

not every CHEM4 student would be familiar with solid state electronic structure.

Basically I wanted the answer: for a p-n junction, with V (valence) and C (conduction) bands then the 4 level sequence is

pV  (electrical excitation) pC  (electron/hole motion) nC (laser action) nV ~> pV

Any reasonable discussion of this system attracted full marks!

2) Use the attached Figure from the lectures on REMPI-TOF-MS:

  1. to show that the TOF of the mass peaks in the figure have the expected relationship to the mass of the species.
  2. to make an estimate of the vibrational frequency and anharmonicity of the excited state of I2 being studied.

a. The relationship between time and mass in the TOF spectrum is time ~ (mass)1/2.

The 4 peaks in the spectrum:

Species / Mass / Mass1/2 / Time / Time/ Mass1/2
I / 127 / 11.26 / 12.6 / 1.12
I-Ar / 167 / 12.92 / 14.3 / 1.11
I2 / 254 / 15.94 / 17.6 / 1.10
I2-Ar / 294 / 17.15 / 19.0 / 1.11

The final column is sufficiently constant to prove the point (given the limited accuracy of reading times of the figure).

b.The 8 peaks (the origin peak is the first weak feature) are at energies (as accurately as can be measured off the spectrum, which is not very accurate):

53380 (not accurate) / separation:
53580 / 200 (?)
53820 / 240
54070 / 250
54310 / 240
54540 / 230
54775 / 235
55020 (least accurate) / 245(?)

The vibrational frequency from this data is 240 +/- 10 cm-1 and there is no evidence of convergence on a dissociation limit therefore the anharmonicity is ~ 0 cm-1 from this data.

3) The 2s  2p transition of Li atoms is observed at 670.785 nm. Given that the ionization energy of the atom is 43487.15 cm-1, calculate the quantum defect of the 2p state; predict the wavelength at which the 2s  3p transition will be observed; name a dye that could be used in a dye laser to excite the 2s  2p transition.

670.785 nm  14907.9 cm-1 = hυ

hυ = IP – R / n* 2, R = 109737 cm-1

n* = 1.959 = n – δ = 2 - δ

δ = 0.040

n* (3p) = 3 – 0.040 = 2.959

hυ = IP – R / n* 2 = 30953.9 cm-1  323.061 nm

A Laser dye that is intense in the region of 670.785 is LC 6500, Sulforhodamine (there are others)

4) A laser delivers a 1 mJ pulse of 690 nm radiation with a pulse width of 5 fs at a frequency of 50kHz. What is the power of the laser (a) during one pulse, (b) on average? How many photons are emitted per pulse? If, in a multiphoton generation process, a photon is generated that has the same energy as 21 of these fundamental photons, what is the wavelength of that photon?

a) Energy in 1 pulse = 1 x 10-3 J , time duration of 1 pulse = 5 x 10-15 s

Power = energy/time = 2 x 1011 Js-1=200 GW

b) In 1 sec, 50k pulses deliver 50 J, average power = 50 W

Energy per photon = hc / λ = 2.8885x10-19 J

Photons per pulse = 1 x10-3 / 2.8885x10-19 = 3.465 x1015

Easy method: energy ~ 1 / λ, therefore, wavelength of photon with 21 times more energy than 690 nm is 690/21 nm = 32.85 nm (soft x-rays!)