Electronic Structure of Atoms

Quantum Effects and Photons

Quantum Effects and Photons

What's the difference between a "red hot" poker and a "white hot" poker?

• The pokers are different temperatures ("white hot" poker has a higher temperature)
• The pokers emit different intensities and wavelengths of electromagnetic radiation (especially in the visible spectrum

Max Planck (1900)

Energy can be released (or absorbed) by atoms only in "packets" of some minimum size

• This minimum energy packet is called a quantum
• The energy (E) of a quantum is related to its frequency (n) by some constant (h):

E = hn

• h is known as "Planck's constant", and has a value of 6.63 x 10-34 Joule seconds (Js)
• Electromagnetic energy is always emitted or absorbed in whole number multiples of (h*n)

Calculate the smallest amount of energy (i.e. one quantum) that an object can absorb from yellow light with a wavelength of 589 nm

Energy quantum = hn

so we need to know the frequency n

n l= c

n = c/l

n = (3.00 x 108 m/s)/(589 x 10-9 m)

n = 5.09 x 1014 s-1

plugging into Planck's equation:

E = (6.63 x 10-34 Js)*( 5.09 x 1014 s-1)

E (1 quanta) = 3.37 x 10-19 J

Note that a quanta is quite small. When we receive infrared radiation from a fireplace we absorb it in quanta according to Planck's Law. However, we can't detect that the energy absorbtion is incremental.

On the atomic scale, however, the quantum effects have a profound influence

The Photoelectric Effect

Light shining on a metallic surface can cause the surface to emit electrons

• For each metal there is a minimum frequency of light below which no electrons are emitted, regardless of the intensity of the light
• The higher the light's frequency above this minimum value, the greater the kinetic energy of the released electron(s)

Using Planck's results Einstein (1905) was able to deduce the basis of the photoelectric effect

• Einstein assumed that the light was a stream of tiny energy packets called Photons
• Each photon has an energy proportional to its frequency (E=hn)
• When a photon strikes the metal its energy is transferred to an electron
• A certain amount of energy is needed to overcome the attractive force between the electron and the protons in the atom

Thus, if the quanta of light energy absorbed by the electron is insufficient for the electron to overcome the attractive forces in the atom, the electron will not be ejected - regardless of the intensity of the light.

If the quanta of light energy absorbed is greater than the energy needed for the electron to overcome the attractive forces of the atom, then the excess energy becomes kinetic energy of the released electron.

Since different metals have different atomic structure (number of protons, different electronic structure) the quanta of light needed to overcome the attractive forces within the atom differs for each element

The Photoelectric effect as a carnival game:

A popular carnival game is where you are given a giant mallet and have to hit a pad on the ground. This sends a small metal slug shooting up a vertical track and, if you hit it hard enough, it will hit a bell at the top. This is like the photoelectric effect - if the electron will be released from the atom if it absorbs a photon with enough energy. Imagine that you have a 10 year old child and Arnold Schwartenegger. The child is too weak to hit the pad hard enough to ring the bell. It doesn't matter if you have an army of 10 year olds lined up to take their turn - none of them will ever hit it hard enough to ring the bell. However, Arnold (being Arnold) will have no problem ringing the bell.

Thus, if the light shining on a metal does not have photons with the necessary energy to cause an electron to be ejected, then it does not matter how bright the light is. The key thing is to increase the energy of the individual photons, and this is achieved by increasing the frequency (i.e. decreasing the wavelength)

High energy photons, from x-rays for example, can cause electrons from many atoms to be ejected and with high kinetic energy as well. The release of such high energy electrons can cause tissue damage (cancer).

Radio waves have such a low quanta of energy that even though we are bombarded by them, they do not cause the release of electrons.

Einstein's interpretation of the photoelectric effect suggests that light has characteristics of particles. Is light a wave or does it consist of particles?

1996 Michael Blaber