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Optical Spectroscopy
09 January 2018 10:03
Performance of Usain Bolt in 100m sprint
Motion
• Velocity is the rate of change of displacement
Momentum = mass(m) x velocity(v)
Kinetic energy = 1/2 x mass x velocity2 If Usain Bolt's mass is 86kg, work out the average momentum,
Force = mass(m) x acceleration(a) average kinetic energy and force at the start of the race • Acceleration is the rate of change of velocity
Work = force(F) x distance moved by force(x) • Some values such as Gibbs free energy only depend on
Power = work done(w)/time taken(t) the final and initial value, it doesn't matter what the route Calculate the work (if the force is constant over the race),
Potential energy = mgh taken was to get from the initial value to the final value power, gravitational potential energy (at a height of 1m)
Pressure = force/area • Work done depends on how you get from the initial to and the velocity as Usain Bolt hits the ground.
Moment = force x distance from point 0 final value as there will be different force values
Energy must be conserved, so can be transferred from one form
• The weight of a person on Earth is equal • The pressure acting on the ground is to another e.g. when hits the ground transferred to kinetic energy
to the force due to gravity (g=9.8ms-2) determined by the area over which the force is Moment of force
acting (The area of Usain Bolt's feet is 0.072m2) • The moment of force (or torque) is a measure of how easy it is
to rotate an object about a point
• The system is at equilibrium (with respect to rotation) when the
pivot is positioned so that: F1r1=F2r2
HANDOUT 1 - INTRODUCTION TO OPTICAL SPECTROSCOPY
Learning objectives for this part of the course:
• Know that energy levels are quantised
• Know where on the electromagnetic spectrum rotation, vibration and electronic transitions occur and
understand the difference between absorption and emission spectroscopy
• Know what influences the intensity and width of spectroscopic transitions
• Understand the basic principles behind rotational spectroscopy: moments of inertia, selection rules,
rotational energy levels and transitions, rotation constant (B), rotational energy term (F(J)) Quantisation of Energy
• Be able to determine the rotational constant from a list of rotational transitions and hence determine When an electric charge is passed through gaseous hydrogen,
the moment of inertia (I) and bond length (R) for a linear molecule. Be able to predict rotational the molecules dissociate and the excited atoms emit radiation as
spectrum from moments of inertia or bond lengths. they return back to their ground (lowest energy) state.
• Understand the basic principles behind vibrational spectroscopy: simple harmonic oscillator (SHO), • Difference in energy is released as a photon of frequency,
force constant (k), selection rules, vibrational energy levels and transitions, fundamental vibrational which is dependent on ΔE
frequency (ωe) normal modes for linear and non-linear molecules, vibrational energy term (G(v)).
• Understand what anharmonicity is and how it influences the vibrational spectrum, selection rules and
the rotational constant B. This relation is called the Bohr frequency condition
• Understand the origins ro-vibrational spectroscopy, know what P, Q, and R transitions are and be able • However, only certain frequencies are observed (only
to determine rotational constants (B1 and B0), bond lengths and force constants from spectroscopic certain energy values are allowed) e.g. the recorded
data frequencies from the emission spectrum of the hydrogen
atom:
The electromagnetic spectrum • Components of the spectrum are referred to as "lines" and their position
• Light is described as in the spectrum is given in wavenumbers (ṽ/cm-1), frequency (v/s-1) or
electromagnetic radiation energy (J)
that propagates as a wave. • Existence of discrete lines in a spectrum indicates that the energy of
• This wave travels at the electrons in the hydrogen atom are quantised.
speed of light, c, • Schrodinger's equation can be solved for a hydrogen atom proving that
(3x108ms-1) the electron in a hydrogen atom can only have certain energies
and is made up of a magnetic and electric component.
• Electromagnetic field is characterised by a wavelength, λ, and frequency, v. Quantum mechanics
• Planck accounted for the behaviour of black-body radiation by proposing that the
De Broglie relation oscillation of the electromagnetic field for a particular wavelength can only be
• According to the de Broglie relation, simulated if a certain energy is provided.
particles with low momentum have long • Proposed that the energy of an oscillator of frequency v is restricted to an integral
wavelengths and particles with high momentum have short wavelengths. multiple of the quantity hv:
• Large objects such as a cricket ball have such large momenta, even if they • Photons are discrete particles of light that travel at the speed of light with energy hv.
are moving very slowly, they have undetectably short wavelengths. Hence
they do not behave as waves. Heisenberg's uncertainty principle
Flame test Types of spectroscopy • Although we can determine the momentum of a wave-like particle
Boron - green Absorption spectroscopy and emission we cannot also determine its position accurately. Likewise, cannot
Sodium - yellow/orange spectroscopy: determine accurately the momentum of a particle if we measure its position.
Lithium - red • Heisenberg uncertainty principle: it is impossible to specify simultaneously, with
Magnesium - white precision, both the momentum and the position of a particle.
Potassium - purple
Copper - depends on The electromagnetic spectrum and the nature of light
oxidation state (green/blue) • Electromagnetic radiation comprises electric and magnetic fields oscillating at
right angles to each other and to the direction of propagation:
• Spectroscopic lines arise form transitions between energy levels • Wavelength, lambda λ
Physical Chemistry I Page 1
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