hydrogen that lie outside of the visible spectrum, which are predicted by formulas very

similar to the one in Equation 1.

Later scientists determined that similar relationships existed for the spectral lines of

other elements, as stated by the Rydberg-Ritz combination principle. Although the

hydrogen atom is often used to discuss this principle in order to keep things simple, it

applies to all atoms. For instance, the neon sign you see in the photograph above is

displaying red light at the wavelengths of several of its spectral lines.

The physicists who determined these mathematical relationships did not know why the

wavelengths of the spectral lines followed the patterns they did. These data were just

too far ahead of the theory of atomic structure. Scientists could observe the discrete

spectral lines of the emitted and absorbed light, and note the mathematical relations

that predicted their wavelengths, but could only speculate as to the cause.

However, the work was underway. The light emitted by hydrogen was found to have a

discrete spectrum, one that could be predicted by a formula. It was a tantalizing clue

about the quantized nature of atoms.

What is the lowest visible

frequency of light emitted by

hydrogen?

f = 4.57×10^14 Hz

36.3 - Photons

Photon: A packet of light. The fundamental

unit or quantum of light.

Max Planck showed how the radiation emitted by an ideal object in thermal equilibrium

with its surroundings could be explained if the radiation emitted or absorbed by the body

was quantized. His theory had a somewhat marginal existence for four years until Albert

Einstein, then employed as a Swiss patent clerk, began to consider it in depth.

Planck’s theory stated that the energy (radiation) absorbed or emitted by an object

had to be taken up or released in discrete chunks, as quanta. However, he still

conceived of the radiation itself as a wave. His theory simply stated that matter

absorbed or emitted the radiation in discrete amounts.

Einstein took the next bold step: He stated that the radiation itself was quantized. He

saw that what Planck had been studying was not just how matter absorbed and emitted

radiation, but the basic nature of the radiation itself.

Einstein stated that light of any frequency is quantized in units now called photons. The

energy of a photon is proportional to its frequency f.

He wrote, “The energy in a beam of light is not distributed continuously through space, but consists of a finite number of energy quanta, which

are localized at points, which cannot be subdivided, and which are absorbed or emitted only as whole units.” (This was in the same year that

he published his special theory of relativity; not a bad year.)

This new model challenged the previous concept that light behaved solely as a wave. Instead, it stated that light could also be conceived of as

a stream of packets of energy, almost as particles.

The energy of each photon could be calculated with the equation E = hf. In other words, red light of frequency 4.60×10^14 Hz cannot have just

any energy level; its energy is always an integer multiple of hf. One photon of red light of frequency 4.60×10^14 cycles per second has

3.05×10í^19 J of energy, two photons of this frequency red light have 6.10×10í^19 J of energy, and there is no such thing as 1.5 photons of red

light, any more than there can be 1.5 electrons.

Pre-Einstein conception of light

Light is a wave

·Energy can vary continuously

·Einstein demonstrated flaws in the

wave model of light

(^662) Copyright 2007 Kinetic Books Co. Chapter 36