Anupam MisraHIGP, University of Hawaii, Honolulu, USA

Spectroscopy: Lecture 2

Atomic Spectra

www.soest.hawaii.edu\~zinin

GG 711: Advanced Techniques in Geophysics and Materials Science

Atomic Spectra

• Absorption spectroscopy (UV-VIS, IR, Fraunhofer lines, atmospheric studies,..)

• Emission spectra(Calibration lamps Ne, Hg, flames, explosion, sun, stars, LIBS: Laser induced breakdown spectroscopy)

Flame tests

http://www.nasa.gov/mission_pages/messenger/multimedia/mercury_telecon_20081029.html

Example sodium and calcium emissions detected by the Mercury Atmospheric and Surface Composition Spectrometer (MASCS) instrument on the MESSENGER spacecraft during the second Mercury flyby.

Emission spectra of atoms

Atomic spectra:

* Why so many lines: it has only 1 electron ?

* Simplest atom is Hydrogen atom

www.solarobserving.com/halpha.htm

Absorption spectra

Emmision spectra

Bohr’s model of atom;

1. Every atom consists of nucleus and electrons revolved around the nucleus in circular orbits.

2. Electrons revolved only in certain non-radiating orbits called stationery orbits for which the total angular momentum is an integral multiple of h/2π where h is plank's constant.

L is the Angular momentum of the revolving electrons.

L = r x p = r x mV

= mvr sin 90 = mvr = n h/2π

3. Radiation occurs when an electron jumps from one permitted orbit to another. It is emitted when electron jumps from higher orbit to a lower orbit

i.e., E2 - E1 = hf, where f is frequency of radiation.

Postulates:

De Broglie wave

2 π r = n λ

= n h/ (mv)

mv r = n ħ

p = h / λ = ħk k = 2 π/ λ

k = 1/ (4 πεo) = 9 x 109 Nm2/C2

Bohr Radius

r ∝ n2

Bohr Radius.

J

www.physics.udel.edu/.../images/hydrogen.gif

www.physics.fsu.edu/.../images/hydrogen.gif

Hydrogen energy levels:

-13.6 eV

0 eV

Q 1: Line C observed at 656.3 nm in Fraunhofer lines correspond to Hydrogen. Identify this transition.Q 2. Can we see the Lyman series transition n = 2 to n = 1 with our eye?

1 eV = 1.6×10−19 Joulesh = 6.6×10−34 Joules.secc = 3×108 m/s = 299 792 457 m/s

E = h νc = λ ν

Photon energy E, frequency ν, wavelength λ,

532 nm (green light) corresponds to 2.33 eV.

1 eV corresponds to 1240 nm (infra red)

13.6 eV would corresponds to 91 nm (deep UV)

Bohr model: The energy of the n-th level is:

* Simplest atom is Hydrogen atom

En

n = 1, 2, 3, ...., denoting energy;

l = 0, 1, ..., n-1, denoting angular momentum;

m = -l, ...., l, denoting orientation (the "magnetic quantum number"),

s = -1/2, 1/2, denoting spin (m s is also used in place of s).

s, p ,d , f…for l = 0, 1, 2, 3…

K, L, M, N…for n = 1, 2, 3, 4, …

Kα line is transition from n = 2 to n = 1 (L to K level)Kβ line is transition from n = 3 to n = 1 (M to K level)

http://www.flickr.com/photos/clementi/3278124162/

E = ħ ω = h f

formulae to remember

p = ħ k = h / λ

c = f λ E = pc (for photon)

ω = 2 π f

k = 2 π / λ

NIST Atomic Spectra Database Lines Data

NIST Atomic Spectra Database Lines Data

NIST Atomic Spectra Database Lines Data

Homework:

Q1. Calculate the frequency and wavelength of the photon emitted when anelectron of 20 keV is brought to rest in one collision with a heavy nucleus.(x-ray production).

Q2. Find the maximum wavelength of the photon that will separate a molecule whose binding energy is 15 eV.

Q3. A 93.1 MHz radio station of 200 kW output generates how many photons in 1 minute?

Q4. Find the energy and wavelength of two photons that are produced when annihilation occurs between an electron and positron that are initially at rest.

From Wikipedia: Wave vector k