The explanation for blackbody radiation and, in particular, the shape of the radiation curves, could not be found in classical physics.  For example, classical physics predicts that as an object heats up it should start releasing energy in shorter and shorter wavelengths, because this is the most efficient way to release energy.  At very high temperatures, the amount of energy released is maximized by the release of ever-shorter wavelengths.

 



 

 

 

However, the blackbody radiation curves produced by hot objects show that even at extremely high temperatures, most of the energy is released by relatively long wavelengths with little or no energy released by very short wavelengths.  The explanation for the shape of the observed curves came from Max Planck in the year 1900.  He could account for the shape by assuming that there was a specific amount of energy that any given wavelength of radiation could exchange with its environment.  The term  quantum  refers to this specific energy, and it is related to the wavelength of the radiation by  Planck's formula .



Quantum ( pl.  quanta):  the smallest bundle or packet of energy that a given wavelength or frequency of EMR can possess





Planck's formula:  EMR energy is the product of the number of quanta, Planck's constant, and the frequency of the radiation

E=nh


Quantity

Symbol

SI Unit

quantum energy

E

J

Planck's constant

h

6.63 × 10 -34 J*s

or

4.14 × 10 -15 eV*s

frequency

f

Hz or /s

number of quanta*

n

no units










 * n refers to the whole number of quanta that make up the total amount of energy ( ) transferred by the radiation; therefore, = 1, 2, 3, 4, . . . .

Note that Planck's formula applies equally to wavelength as it is related to frequency by the universal wave equation.

c=fλf=cλ

Planck's formula represents a fundamental shift in theory.  In this system the amount of energy that can be exchanged between radiation and its surroundings is quantized, or limited to whole-number multiples of the smallest unit of energy-the quantum.  Furthermore, the value of each quantum is equal to the product of Planck's constant and the frequency of the radiation ( hf ).  The concept of the quantum effectively ended classical physics and gave birth to quantum physics.

Several years later Albert Einstein proposed that radiation, including visible light, could be quantized regardless of whether or not it exchanges energy with its surroundings.  In 1926 chemist Gilbert Lewis introduced the term photon  to describe a single quantum of light.  The energy of one photon is given from Planck's formula and is  E  =  hf .


photon:  one quantum of light



Read
Read "Einstein, Quanta, and the Photon" on page 706 of the textbook.


Try This

Complete the following "Practice Problems" from the text:

- Questions 1, 2, and 3 on page 706

- Questions 1, 2, and 3 on page 707

- Questions 1 and 2 on page 708


Energy and the Spectrum

Planck's formula associates photon energy with the frequency of radiation, expanding the electromagnetic spectrum to show the energy of various classifications of EMR.