Photonics in Food Science ICTP Trieste, Italy Laser spectroscopy - PowerPoint PPT Presentation

Winter College on Applications of Optics and Photonics in Food Science – ICTP Trieste, Italy Laser spectroscopy for gas sensing Luca Poletto CNR - Institute for Photonics and Nanotechnologies Padova, Italy 1

The term SPECTROSCOPY denotes methods where the interaction of light with matter is utilized. The strength of some interaction (e.g. absorption of light) is measured as a ~  1 function of the photon energy E = h n, or wavelength l, or wavenumber n l Some quantities photon energy wavelength wavenumber m m cm -1 eV 6.2 - 3.1 0.2 - 0.4 50000 - 25000 Ultraviolet 3.1 - 1.55 0.4 - 0.8 25000 - 12500 Visible 1.55 - 0.41 0.8 - 3.0 12500 - 3300 Near IR 0.41 - 0.025 3.0 - 50 3300 - 200 Mid IR

SOME USEFUL RELATIONS n = photon frequency w = 2 pn = angular frequency E = h n = photon energy l = c/ n = photon wavelength c = speed of light in vacuum  3  10 -8 m/s h = Planck’s constant = 4.14  10 -15 eV  s 1 eV = 1.6  10 -19 J l ( m m) = 1.24 / E (eV) ~ n (cm -1 ) = 10000 / l ( m m)

ATOMIC ABSORPTION IN ATOMS Wave-matter interaction in atoms  transfer of energy from photons to electrons  excitation of electrons from one atomic orbital to another Since the atomic orbitals have discrete specific energies , transitions among them have discrete specific energies. Therefore, atomic absorption spectra consist of a series of “lines” at the wavelengths of radiation that correspond in energy to each allowable electronic transition . Emission and absorption spectrum of sodium: D-lines at 588.995 and 589.592 nm (yellow)

BOHR ATOMIC MODEL ● Negatively charged electron orbits a positively charged nucleus ● The electrons can only orbit stably, without radiating, in certain "stationary orbits" at a discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy levels. In these orbits, the electron's acceleration does not result in radiation and energy loss as it would be required by classical electromagnetism. ● Quantum jump between orbits with help from an absorbed amount of electromagnetic radiation The Bohr model of the Hydrogen Atom

2 2 v Ze Z    Electron speed (from Newton law F =m a ) m v e 2 r r mr 2 2 1 Ze Ze  -  - 2 E mv Energy of the system 2 r 2 r Discretization of the electron orbits h The electron angular momentum is     mr n v n n ( n 1 , 2 , 3 ,...) p quantized 2 2     2 2 r n n n 0.053 nm 2 e mZ p 2 4 Rhc 2 e m   -   Energy levels 2 - 1 E n Z with R 109737 cm 2 3 n h c 2 Z  - E n 13 . 6 eV 2 n 6

Emission or absorption of energy ( D E = h n ) - E E n  n n ' h - E E ~ n  n n ' hc For the H atom (Z = 1)   1 1 n  -   Rc   2 2 n ' n   1 1 ~ n  -   R   2 2 n ' n 7

EXERCISE Calculate the emission lines for the hydrogen atom (Z = 1) for the transitions from level n’ = 1   1 1 Answer: ~ n  -   R   2 2 n ' n R(1-1/2 2 ) = 109737  0.75 = 82303 cm -1  l 1 = 121.5 nm R(1-1/3 2 ) = 109737  0.89 = 97666 cm -1  l 2 = 102.4 nm R(1-1/4 2 ) = 109737  0.94 = 103153 cm -1  l 3 = 97 nm …… R(1-0) = 109737 cm -1  l  = 91.2 nm Limit for n  This is called Lymann series 8

Atomic Hydrogen emission Lyman series n ’= 1, n=2,3,4, … .. Balmer series n ’= 2, n=3,4,5, … .. 9

ATOMIC HYDROGEN EMISSION 10

ATOMS WITH MORE ELECTROS Generalized Bohr’s model  ● Elliptical orbits two quantum numbers to define an ellipse ● Energy levels depend on two quantum numbers  more energy levels than the single atom 11

SPONTANEOUS EMISSION The atom decays from level E2 to level E1 with a certain probability A(2,1) and emits a corresponding photon at frequency n A(2,1) = Einstein coefficient for spontaneous emission from level E2 to level E1 Starting from a level n , the atom can decay to lower levels with a total probability g n . The decay speed is proportional to the numbers of atoms in the level n . dN - g  - g   0 t n N N N e n n n n n dt Time domain: exponential Spectral line profile: lorentzian Fourier transform

LINE PROFILE Natural broadening in brief The uncertainty principle D E D t  h/2 p ( h is the Planck constant) relates the lifetime of an excited state with the uncertainty of its energy. A short lifetime will have a large energy uncertainty and a broad emission. As the excited state decays exponentially in time, this effect produces a line with Lorentzian profile . D E 1 n   p D h 2 t g 1 n  g ( )     p n - n  g p 2 2 2 4 4 0 where G is the total transition probability for the excited level

DOPPLER EFFECT Relative speed between atom and observer n - n n n  cos u    Frequency shift 0 n n c c 0 0  Maxwellian distribution of atoms it describes the particle speeds at thermodynamic equilibrium in idealized gases where the particles move freely inside a container without interacting with one another, except for very brief collisions -  m   2  dw exp u du Distribution of atoms within a speed interval du   2 kT The Doppler shift at a certain frequency is proportional to the particles (atoms/molecules) that are moving at a velocity u giving n/n = u/ c 14

Doppler broadening in brief The atoms in a gas have a distribution of velocities. Each photon emitted will be shifted in frequency by the Doppler effect depending on the velocity of the atom relative to the observer. The higher the temperature of the gas, the wider the distribution of velocities in the gas. Since the spectral line is a combination of all of the emitted radiation, the higher the temperature of the gas, the broader the spectral line emitted from that gas. This broadening effect is described by a Gaussian profile . -  n 2 2 mc n    I ( ) exp n 2   2 kT 0 n l 8 ln 2 8 ln 2 kT kT n l     0 0 d d c m c m m = atomic mass k = Boltzmann constant

EXERCISE Calculate the natural broadening and the Doppler broadening for the H atom at the transition Lymann- a at 121.5 nm at T = 1000 K (electric discharge). The average life of the excited state is t  0.16  10 -8 s 1 Natural broadening n  p n  1  10 8 Hz = 0.1 GHz D 2 t Doppler broadening n d = 1/(121.5  10 -9 )  [(5.55  1.3  10 -23  500/(1.8  10 -27 )] 0.5 = 5.6  10 10 Hz = 56 GHz n 8 kT ln 2 1 8 kT ln 2  n   l d where c m m K = Boltzmann constant = 1.3  10 -23 J/K m = hydrogen mass = 1.8  10 -27 kg Doppler broadening is 1-3 orders of magnitude higher than the natural broadening (depending on element, transition, temperature)

COLLISION EFFECT Natural emission from an atom is disturbed by collisions  phase and amplitude of the emitted radiation change  the duration of the unperturbed emission is reduced  the line width is increased 1 n  t 0 average time between collisions I ( )     n - n  pt 2 2 1 2 0 0  n  pt 1 / 2 c 0 From kinetic gas theory  n 2 kT  = cross section for collisions (m 2 )  n   p 2 p c m n = density of particles (m -3 ) m = mass 17

Pressure broadening in brief The collision of other particles with the emitting particle interrupts the emission process, and by shortening the characteristic time for the process, increases the uncertainty in the energy emitted. This effect depends on the density of the gas, hence on pressure. The broadening effect is described by a Lorentzian profile .

EXERCISE Calculate the collisional broadening for the H atom, 1 atm, atom density n = 7.2  10 24 m -3 at the transition Lymann- a at 121.5 nm at T = 1000 K (electric discharge). The collisional cross section at 121.5 nm is   10 -19 m 2 Collisional broadening n c  5  10 8 Hz = 0.5 GHz   n 2 kT p N 2 k  n   A p p c 2 m 2 R Tm where K = Boltzmann constant = 1.3  10 -23 J/K m = hydrogen mass = 1.8  10 -27 kg N d pN   A A n M RT Collisional broadening is higher than natural broadening and depends on gas pressure.

Total broadening A combination of the different causes gives a Voigt profile  convolution between a Gaussian and a Lorentzian The Voigt profile is dominated by the Gaussian in the center and by the Lorentzian in the wings

LINE PROFILES IN GASES For gas absorption lines in standard conditions (atmospheric pressure and ambient temperature), the line profile is dominated by collision broadening (lorentzian profiles). Example Pressure broadening at room temperature for the oxygen lines in the A band (760 nm or 13122 cm -1 ) accounts for a typical broadening of 0.05 cm -1 /atm. At room temperature and ambient pressure, the measured linewidth is around 2 GHz with a line profile that is largely lorentzian.