Quantum Mechanics

Photoelectric Effect & The Ultraviolet Catastrophe

Birth of Quantum MechanicsUntil about 1900, scientists only understood electromagnetic radiation to be made up of waves. Then in the early 1900s Max Plank theorised that light was quantised, that it came in discrete packages.

Max Planck stated that the light emitted by a hot object (black body radiation) is given off in discrete units or quanta. The higher the frequency of the light the greater the energy per quantum.

Quantum?

Quantum mechanics is the study of processes which occur at the atomic scale.

The word "quantum" is derived From Latin to mean BUNDLE.

Therefore, we are studying the motion of objects that come in small bundles called quanta. These tiny bundles that we are referring to are electrons traveling around the nucleus.

Li Na K

Different atoms emit distinct light

Black Body RadiationHot objects emit radiation. The hotter they are the more they emit, at higher energies. Thus hot objects show a characteristic pattern of light emission. This sort of radiation is called black-body radiation.

Black Body RadiationThe term "black body" is used because none of the light is reflected from some other source and the intrinsic color of the material is not important. A bar of gold and a bar of black graphite at 3000 degrees C would emit the same color light. The Sun is very close to a theoretical black body in its light emission - all stars are. The Moon is not. The Moon absorbs sunlight and re-emits it in different forms, for example, a lot of visible light is absorbed by the surface and re-emitted in infrared. Incandescent lights, as befits their names, are pretty close to black-body emitters, fluorescent, neon, and sodium-vapor lights are not.As temperature increases, two things happen:The object emits more radiation at all wavelengths.The peak of maximum emission shifts toward higher-energy (blue) wavelengths. The very hottest stars emit most of their radiation in the ultraviolet.As an object heats up, the peak of emission creeps into the visible range and the familiar "red hot" color appears. As the object gets still hotter, the peak shifts into the yellow part of the spectrum and the object glows orange, then yellow. But then the object becomes a paler yellow and finally white, not green. Why? When the emission peak is in the green (as it actually is for the Sun!), the object is still emitting copious red and yellow light, and these wavelengths combine to give a fairly pure white. But the very hottest stars have peaks in the violet and beyond, and their blue and violet emission is so much greater than their red and yellow that the stars appear blue-white.

This was a CLASSICAL prediction, first made in the late 19th century, that an IDEAL BLACK BODY at thermal equilibrium will emit radiation with INFINITE POWER.

Max Planck resolved this issue by postulating that electromagnetic energy did not follow the classical description, but could only oscillate or be emitted in DISCRETE PACKETS OF ENERGY proportional to the frequency. He called these packets ‘QUANTA’.

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The Ultraviolet Catastrophe

Plank’s ConstantPlanck’s constant, (symbol h), fundamental physical constant characteristic of the mathematical formulations of quantum mechanics, which describes the behavior of particles and waves on the atomic scale, including the particle aspect of light. The German physicist Max Planck introduced this constant in 1900 in his accurate formulation of the distribution of the radiation emitted by a blackbody, or a perfect absorber of light. The significance of the context is that radiation, such as light is emitted, transmitted, and absorbed in discrete energy packets, or quanta, determined by the frequency of the radiation and the value of Planck’s constant.

The energy E of each quantum, or each photon, equals Planck’s constant h times the radiation frequency symbolized by the Greek letter nu, ν, or simply E = hν. The dimension of Planck’s constant is the product of energy multiplied by time, a quantity called action. Planck’s constant is often defined, therefore, as the elementary quantum of action. Its value in metre-kilogram-second units is 6.62606957 × 10−34 joule second, with a standard uncertainty of 0.00000029 × 10−34 joule second.∙ ∙

Light is a ParticleAlbert Einstein, one of the few scientists to take Planck's ideas

seriously, proposes a quantum of light (the photon) which behaves like a particle in 1905. Therefore, light

consisted of photons.

A photon is a “particle” or “packet” of energy.

A photon has an energy of E = hf where h is called Planck’s constant

and f is frequency.High frequency (low wavelength)

photons have high energy; low frequency (high wavelength) photons

have low energy.

“Newton, forgive me..”, Albert Einstein

At the atomic scale Newtonian Mechanicscannot seem to describe the motion ofparticles. An electron trajectory betweentwo points for example IS NOT a perfectparabolic trajectory as Newton's Lawspredicts. Where Newton's Laws endQuantum Mechanics takes over.....IN ABIG WAY!

One of the most popular concepts concerning Quantum Mechanics is called , “The Photoelectric Effect”. In 1905, Albert Einstein published this theory for which he won the Nobel Prize in 1921.

Properties of Photons

Electromagnetic radiation

can be viewed as a stream

of particle-like units called

photons

POSTULATE

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The photoelectric effect.

Work FunctionWork function, f, is defined as the least energy that must

be supplied to remove a free electron from the surface of the metal, against the attractive forces of surrounding positive ions.

Shown here is a PHOTOCELL. When incident light of appropriate frequency strikes the metal (cathode), the light supplies energy to the electron. The energy need to remove the electron from the surface is the WORK!

Not ALL of the energy goes into work! As you can see the electron then MOVES across the GAP to the anode with a certain speed and kinetic energy.

Maximum K.E.The MAXIMUM KINETIC ENERGY is the energy difference between the

MINIMUM AMOUNT of energy needed (ie. the work function) and the LIGHT ENERGY of the incident photon.

THE BOTTOM LINE: Energy Conservation must still hold true!

Light Energy, E

WORK done to remove the electron

The energy NOT used to do work goes into KINETIC ENERGY as the electron LEAVES the surface.

Photoelectric effect

Photoelectric Effect

The emission of electrons from a surface (usually metallic) upon exposure to, and absorption of, electromagnetic radiation.

The photoelectric effect was explained mathematically by Einstein who extended the work on QUANTA as deloped by Planck.

Photoelectric Effect

– The photoelectric effect is the ejection of electrons from the surface of a metal when light shines on it.

Quantum Effects and Photons

– Electrons are ejected only if the light exceeds a certain “threshold” frequency.

– Violet light, for example, will cause potassium to eject electrons, but no amount of red light (which has a lower frequency) has any effect.

Phot

o El

ectr

ic E

ffect

Photoelectric effect

– For a given metal, a certain amount of energy is needed to eject the electron

– This is called the work function

– Since E=hn, the photons must have a frequency higher than the work function in order to eject electrons

Planck’s Constant

hcEf

c

hf

EhfEfE

h hc

6.63x10-34 Js 1.99x10-25 Jm

4.14x10-15 eVs 1.24x103 eVnm

Make sure you USE the correct constant!

Planck’s Constant is the SLOPE of an Energy vs. Frequency graph!

Threshold FrequencyThe frequency of radiation must be above a certain value before the

energy is enough. This minimum frequency required by the source of electromagnetic radiation to just liberate electrons from the metal is known as threshold frequency, f0.

The threshold frequency is the X-intercept of the Energy vs. Frequency graph!

Equations

bmxy

hfKWhfK

hfWK

hfE

KINETIC ENERGY can be plotted on the y axis and FREQUENCY on the x-axis. The WORK FUNCTION is the y – intercept as the THRESHOLD FREQUNECY is the x intercept. PLANCK‘S CONSTANT is the slope of the graph.