Electromagnetic radiation

Atomic Hydrogen Spectrum and the Bohr Model of the atomSCH 100Lecture 31Why know something about electromagnetic radiation?Much of what we know about atoms/matter comes from studying the interaction of radiation with matter spectroscopy.Radiation is a wave phenomenon. a wave is a disturbance that travels through space and time, usually accompanied by the transfer of energy. They can be mechanical propagates through a mediumelectromagnetic can travel through a vacuumNature of Electromagnetic radiation2Characteristics of WavesWavelength, measured in mFrequency, measured in HzAmplitude, A, measure in m

3Relationship between frequency and wavelengthElectromagnetic radiation moves through vacuum at a speed of 2.998x108ms-1 which is called the speed of light c.The wave length and frequency are related by:

Where c = velocity of light in vacuum = 2.998 x108 m/s, = wavelength of radiation = frequency of radiation

4Nature of Electromagnetic radiationElectric componentMagnetic component

Electromagnetic5Complete Electromagnetic spectrum

Consists of all the frequencies or wavelengths of electromagnetic radiation from the longest tv or radio waves to the very shorted gamma rays:6Common units of wavelengthUnitSymbolLength /mType of radiationAngstrom10-10X-rayNanometernm10-9Ultraviolet, visibleMicrometer10-6InfraredMillimetermm10-3InfraredCentimetercm10-2MicrowaveMeterm10TV, radio7Plancks hypothesisWhen radiation interacts with matter, Energy is absorbed or emitted only in discrete amounts known as quanta and not continuously.Each quantum of energy is given by the equation E = hnWhere n is the frequency of the radiation and h is Plancks constant = 6.626 x10-34 JsThe equation suggests: Energy associated with any radiation is proportional to its frequency n Energy is quantized8Atomic Hydrogen SpectrumSpectrum - a graph of intensity against frequency or wavelength of radiation absorbed or emitted.Absorption SpectrumEmission spectrumWhen an electric was passed through a tube containing hydrogen gas at low pressure it, a pink glow was observed.What was the source of the glow?9Atomic hydrogen spectrum

10When the pink glow was allowed to pass through a prism, four distinct line could be seen.

The atomic hydrogen spectrum11What was the source of these lines?Is there a mathematical expression that fits the lines in the spectrum?

In 1885 Balmer developed the equation = wavelength of linen = integer with value = 3,4, 5, ., k = a constant 12In terms of wavenumbers the equation rearranges to

13Balmer, 1885Balmer series of lines was obtained

14More invisible lines were discovered in the UV, and IR regions of the electromagnetic spectrum.Rydberg developed the universal equation

This gives the atomic hydrogen spectrum:

15Atomic hydrogen spectrumSeriesRegionn1n2LymanUltravilotet12, 3, 4, 5..BalmerVisible23, 4, 5, 6..PaschenNear infrared34, 5, 6, 7..BrackettFar infrared45, 6, 7, 8..PfundFar infrared56, 7, 8, 9..What was the origin of these lines?16Bohr Model of the Atom (1913)Electrons revolve in orbits of specific radius around the nucleus without emitting radiationWithin each orbit, each electron has a fixed amount of energy and angular momentum given by mvr = h/2; Electrons in orbits further from the nucleus have greater energies.17In order to explain the hydrogen spectrum, Bohr made the following assumptions governing the behaviour of electrons:Bohr Model of the Atom (1913)An electron may jump from one orbit of high energy to another of lower energy causing the energy difference to be emitted as a photon of electromagnetic radiation such as light.

e-h18An electron may absorb a photon of radiation and jump from a lower-energy orbit to a higher-energy one. Energy change involved is given by;e

+ h

19Bohrs ModelNucleusElectronOrbitEnergy Levels2020The Bohr Atom

21Energy levels22

Failures of the Bohr TheoryWhile the model was a major step towards understanding the quantum theory of the atom, it is not in fact a correct description of the nature of electron orbit.

Some of the shortcomings of the models are:-It fails to provide any understanding why some spectral lines are brighter than others.There is no mechanism for the calculation of transition probability.The Bohr model treats electrons as if they were miniature planets with definite radius and momentum. This is a direct violation of the Heisenberg uncertainty principle which dictates that position and momentum cannot be simultaneously determined.2323The Bohr model however, helped in explaining the spectra of hydrogen-like (single electron around a positive nucleus) atoms.It gives a form of physical image of an atom24The Photoelectric EffectThe ejection of electrons from certain metal surfaces when irradiated with high energy electromagnetic radiation like ultraviolet light.First recognized by Heinrick Hertz in 1887.Hertz had observed that, under the right conditions, when light is shined on certain metal surfaces, electrons are released.25Characteristics of PENo electrons ejected by radiation unless its frequency exceeds a threshold frequency value, o characteristic of each metal.The kinetic energy of the emitted electrons is linearly dependent on the frequency of the incident light but is independent of the intensity of the incident light.The Photoelectric EffectClassical physics could not explain these observations

26Explanation of the PEEinstein (1905) used Plancks quantization theory to explain PE. He proposed that radiation consisted of particles or corpuscles (now known as photons after GN Lewis).Each photon had a quantum of energy h.Collision of a photon with an electron on the metal surface gave part of its energy to just strip the electron from the surface and the rest appeared as kinetic energy of the electron.Nobel prize in Chemistry 192327Millikans Experiment

Used alkali metals, Li. Na, and K and measured the maximum kinetic energy as a function of frequency of incident radiation. Straight line graphs were obtained .Slope of the straight line = tan q = h = 6.55 x 10-37 ergs secIntercept of the horizontal axis = Wo/h. Thus the threshold frequency vo is given by

Radiation has Particulate nature

28Conclusions28

Kinetic energy of the electrons can be measured by adjusting the potential on the anode until no current is recorded on the current indicator. The measured voltage (eV) is called the stoppage voltage and must be equal to the kinetic energy of the electrons ejected.eV = mv2 = K = h Wo Wo = minimum energy required to dislodge the electron from the metal29