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Quantum theory of radiation

When a substance is heated it gives out radiation. As it gets hotter and hotter so the radiation emitted has a shorter and shorter wavelength. Actually there is a spread of wavelengths emitted and it's the majority of the radiation that is emitted at shorter wavelengths as the temperature rises.




When it gets hot enough this radiation is so short that it appears as visible light. For many years scientists had struggled to explain the spread of emitted energy with temperature but without success. They wanted to know why a hot piece of metal glowed first red, then orange then yellow and finally white as its temperature was increased. Why cool stars were red and ones that were hot were bluish white.


In 1900 the problem was solved in a revolutionary way by a professor from Berlin University, Max Planck. Planck was born in 1858 in Keil, was educated in Munich and Berlin, becoming a professor in Keil in 1885 before moving to Berlin in 1889. He described his radiation formula as "lucky" but it involved one vital new proposal - that radiation was emitted not in a continuous stream of energy but in bundles of energy that he called quanta. He even related the energy of a quantum to its frequency by the formula:


Energy (E) = h x frequency (f)

where h is a constant known as Planck's constant. This constant can now be measured in school and its value is 6.626 x 10-34 Js.
Planck reasoned that this formula covered all electromagnetic radiation.
We use nano metres (nm) when dealing with the wavelengths of radiation. 1 nm = 10-9 m
The quantum theory and the classical theory is like buying wine in bottles or from a tap. The bottles represent the quantum idea and the continuous flow from the tap represents the classical wave theory. It's also rather like the kangaroo motion of a car when you first learn to drive it jumps from one energy state to another, there is no smooth acceleration.
Although all energy is quantised we are not aware of this in everyday life because of the very small value of Planck's constant.


Problem
If all objects emit radiation why can't we see everything in a darkened room?

Example problem
Yellow light, wavelength 600 nm has a frequency of 5x1014 Hz and so the energy of photon of yellow light is : Energy = hf = 6.63x10-34x5x1014 = 3.31x10-19 J


Now this is a very small energy and so we often use a smaller unit called the electron volt (eV).
An electron volt is defined as the energy gained by an electron when it is accelerated through a potential difference of 1 Volt.
It is a very small amount of energy and since energy (joules) = p.d(volts) x charge(coulombs)

1 eV = 1Vx1.6x10-19 C = 1.6x10-19 J

Returning to the example of the yellow light you can see that the energy of one quantum of yellow light in eV is:

Energy = [3.31 x 10- 19]/1.6 x 10-19= 2.07 eV



This shows that the electron volt is a very useful unit when dealing with emitted radiation.

Example problem
We can use this idea to calculate the number of photons (a word used to describe a quantum of visible radiation) emitted by a 100 W yellow light per second.

Energy emitted by the light bulb every second = 100 J
Energy of each quantum = 3.31x10-19 J
Therefore number emitted per second = 100/3.31x10-19 = 3.0x1020 photons per second.

It is quite obvious that the energy of each quantum must be very small otherwise they would hurt! Imagine being hit by 1020 marbles every second. This would be one of the consequences of life if the Planck constant was large say as big as 1.

The electron volt is a useful unit when measuring the energy of a quantum of light emitted from atoms but sometimes we need to deal with larger quantities of energy and for this reason the keV (103 eV), MeV (106 eV) and GeV (109 eV are used when expressing the energies of high energy such as those of particles from accelerators.

 
 
 
© Keith Gibbs 2013