Energy LevelsPlank’s and Einstein’s quantum theory of light gives thekey to understanding the regular patterns in line spectraPhotons in these line spectra have certain energy values,so electrons in those atoms can only certain energy values.The energy level diagramshows a very simple case – itis for an atom in whichthere are only two possibleenergy levels,Excited stateGround statePhoton emittedElectron, shown by the blue dot has the most potentialenergy when it is on upper level, or excited state.On the lower level, or ground state, it has the leastpotential energy2
Energy levels and quantaDiagram shows electron in excited atom dropping fromexcited state to ground state.This energy jump (transition) has to be done as one jumpand is the smallest amount of energy this atom can lose –called a quantum (plural = quanta)Potential energy electron has lost is given out as aphoton.From E = hf (or E = hc/λ) this energy jump correspondsto a specific frequency (or wavelength) corresponding aspecific line in the line spectrum.In an atom, ground state and each subsequent excitedstate correspond to a particular electron shell (orenergy level).3
Energy levels and quantaThe diagram shows an atom with3 electron energy levels. Whatare the photon energies, in eVthat this atom can emit?10 eV5 eVn = 1n = 2n = 3The potential wellIf you fell down a pit of depth 3m, you would lose about2000 J of potential energy (always calculated fromground level = zero pe)At the bottom of the pit, your Ep is 2000 J less thanzero: it is – 2000 JYou could not jump out, as the maximum kinetic energyyou could generate is 1300 JYour total energy would be 1300 J + (-2000 J) = -700 J4
The potential wellIf the sum of Ek + Ep is negative, we say that thesystem is bound. You are stuck in the pit.This situation is described as the potential wellSimilar situation occurs in an atom. To remove anelectron completely from an atom, enough energy mustbe supplied for the electron to jump from ground stateto the very top of the potential well.It’s the energy needed to overcome the attraction ofthe nucleus and is called ionisation energy5
Energy levels of hydrogenA Danish physicist called NeilsBohr found that hydrogenspectrum could be explainedby a set of energy levelsLowest energy level is theground state, all the othersare excited states.Ground state is a long waybelow the excited states.And excited states get closertogether as you go upwardsn = ∞n = 4n = 3n = 2n = 1E = 0E =-0.85eVE =-1.51eVE =-3.04eVE =-13.61eV6
Energy levels of hydrogenLooking at the energy values of each level: the electronis bound to the atom – does not have enough energy toget out.It requires extra energy to leave the hydrogen atom.Zero potential energy occurs at the very top, electronescapes and leaves an ionised atom.The potential energy of all the levels below E = 0 arenegativeUse the diagram on slide 6 to find the ionisation ofhydrogen7IE = energy of highest level – energy of ground state= 0 eV – (-13.61 eV) = +13 61 eV
Hydrogen emission spectrum8The simple energy leveldiagram on slide 2 hasonly one possibleenergy jump – fromexcited to groundstate.Diagram on slide 4 has3 energy levels and 3possible energy jumpsIn hydrogen with allthose energy levels,there are manypossible transitionsLook at the diagram below
9Arrows all show downward energy transitions, so each wouldgive out a photon – diagram called an emission line spectrumTransitions on the left – going down to ground state, are alllarge. Known as the Lyman series, giving out energeticphotons in UV region of the spectrum.Smaller transitions on the right to n=3 energy level, giveout less energetic IR photons. Known as Paschen seriesBetween these two sets is the Balmer series of lines goingto the n=2 energy level.This series includes the 4 visible lines in the hydrogenemission spectrum, coloured in the diagram.Emission spectra result in electrons dropping down to lowerenergy levels – where did the electron get this energyfrom in the first place?One way is to absorb a photon.
Absorption spectra10ExcitedstateGroundstatePhotonabsorbedThe diagram shows absorption ina simple two-energy level atomExact opposite of emissionspectra, electron starts in alower energy level, absorbs aphoton, which raises it to theexcited state.Photon must exactly match the energy jumpA hydrogen atom has its electron in the energy level at-1.51 eV. It absorbs a photon, which promotes it to the-0.85 eV level. What is the wavelength of this photon.Answer is1.9 x 10-6 m (infra-red region)
11Absorption and emission spectrum of hydrogen
The Sun’s spectrum12The first place an absorption spectrum was observedwas in sunlight. Continuous spectrum from the Sun iscovered with vertical dark lines.These were measured and classified by JosephFraunhofer – Bavarian instrument maker.Lines due to cooler gases in the outer layers of the Sun
13Light from the hot photosphere passes out from the Sun,some light is absorbed by these cooler atoms.Promotes their electrons to excited states. Absorbedphotons must match energy jumps exactly – only certainwavelengths are absorbed.These absorbed photons are re-emitted later in allpossible directions – so fewer photons end up goingdirectly outwards.Spectrum of light becomes dimmer at these wavelengths,because fewer photons are reaching us – giving dark lines.Such spectra are extremely useful for astronomersAbsorption lines in the spectrum of a star or galaxy giveus a ‘fingerprint’ of the elements present.
Stimulated emission• In his analysis of quantum theory, Einsteinrealised that emission and absorption were notthe only possible way to make energy jumps.• An atom already in the excited state can be‘persuaded’ to emit a photon.• Done by a passing photon of exactly the sameenergy.• Produces two identical photons – original oneand the one created by downward transition ofthe electron.• 1st photon stimulated the atom into emitting asecond photon – called stimulated emission.
15This photonstimulatesthe atom......to emit anidenticalphotonSuch a beam of light containingidentical photons ismonochromaticLight is also coherent – phase is constant across the beamThis way of producing extremely regular, uniformradiation was first done with microwaves.A more interesting application uses photons in or near theoptical range – called a laserLight Amplification by Stimulated Emission of RadiationSince their invention in 1958, lasers have become verycommon – in every CD player and DVD player
16Laser light is a narrow, parallel beam which is very intense– scientific usefulness is due to two facts.1. Light is monochromatic – one wavelength only2. Light is coherent – all the waves are in step.Laser action ‘lasing’ can take place in solids, liquids andgases.Before stimulated emission can happen, there must bemore atoms with electrons in the higher excited statesthan in ground state.Under normal circumstances this is the other way round –electrons need to be ‘pumped’ up to the excited state.Often done using an electric field (helium-neon gas laser)See diagram on the board.
17One of the excited atomsemits a photon, at random.This photon stimulatesanother emission. These twophotons then stimulateanother two emissionsThis rapidly becomes anavalanche of identical photonsMirrors at each end reflect the light, making photonspass to and from along the laser.One mirror is partially silvered, so small % of photons cancontinually escape as a laser beam.