Question

8. (a) Two important factors are related to quantum phenomenon: (i) blackbody radiation treatment breaks down at high energies and (ii) photoelectric effect. Why classical physics was not sufficient to explain these phenomenon and quantum physics has to be invoked?

(b) When are quantum confinement effects observed in semiconductor nanocrystallites? What are the implications of quantum confinement for the energy levels?

Answer 1

(a)

Any object with a temperature above absolute zero emits light at all wavelengths. If the object is perfectly black (so it doesn't reflect any light), then the light that comes from it is called blackbody radiation.The energy of blackbody radiation is not shared evenly by all wavelengths of light. The spectrum of blackbody radiation (below) shows that some wavelengths get more energy than others. Three spectra are shown, for three different temperatures.

The explanation of classical physics: Light is an electromagnetic wave that is produced when an electric charge vibrates. (Strictly speaking, "vibrates" means any change in how the charge moves --- speeding up, slowing down, or changing direction.) Now recall that heat is just the kinetic energy of random motion. In a hot object, electrons vibrate in random directions and produce light as a result. A hotter object means more energetic vibrations and so more light is emitted by a hotter object --- it glows brighter. So far, so good. But classical physics could not explain the shape of the blackbody spectrum.

The electrons in a hot object can vibrate with a range of frequencies, ranging from very few vibrations per second to a huge number of vibrations per second. In fact, there is no limit to how great the frequency can be. Classical physics said that each frequency of vibration should have the same energy. Since there is no limit to how great the frequency can be, there is no limit to the energy of the vibrating electrons at high frequencies. This means that, according to classical physics, there should be no limit to the energy of the light produced by the electrons vibrating at high frequencies. WRONG!!Experimentally, the blackbody spectrum always becomes small at the left-hand side (short wavelength, high frequency).

At about 1900, Max Planck came up with the solution. He proposed that the classical idea that each frequency of vibration should have the same energy must be wrong. Instead, he said that energy is not shared equally by electrons that vibrate with different frequencies. Planck said that energy comes in clumps. He called a clump of energy a quantum. The size of a clump of energy --- a quantum --- depends on the frequency of vibration. Here is Planck's rule for the a quantum of energy for a vibrating electron:

energy of a quantum = (a calibration constant) x (frequency of vibration)

or

E = hf

where h, the calibration constant, is today called Planck's constant. Its value is about 6 x 10^-34, very tiny!

So how does this explain the spectrum of blackbody radiation? Planck said that an electron vibrating with a frequency f could only have an energy of 1 hf, 2 hf, 3 hf, 4 hf, ... ; that is,

energy of vibrating electron = (any integer) x hf

But the electron has to have at least one quantum of energy if it is going to vibrate. If it doesn't have at least an energy of 1hf, it will not vibrate at all and can't produce any light. "A ha!" said Planck: at high frequencies the amount of energy in a quantum, hf, is so large that the high-frequency vibrations can never get going! This is why the blackbody spectrum always becomes small at the left-hand (high frequency) side.

The Photoelectric Effect

When light shines on the surface of a metallic substance, electrons in the metal absorb the energy of the light and they can escape from the metal's surface. This is called the photoelectric effect, and it is used to produce the electric current that runs many solar-powered devices. Using the idea that light is a wave with the energy distributed evenly throughout the wave, classical physicists expected that when using very dim light, it would take some time for enough light energy to build up to eject an electron from a metallic surface. WRONG!! Experiments show that if light of a certain frequency can eject electrons from a metal, it makes no difference how dim the light is. There is never a time delay.

In 1905, Albert Einstein came up with the solution. If Max Planck's idea that energy comes in clumps (quanta) is correct, then light must consist of a stream of clumps of energy. Each clump of light energy is called a photon, said Einstein, and each photon has an energy equal to hf (Planck's constant times the frequency of the light). Therefore the energy of light is not evenly distributed along the wave, but is concentrated in the photons. A dimmer light means fewer photons, but simply turning down the light (without changing its frequency) does not alter the energy of an individual photon. So for a specific frequency light, if a single photon has enough energy to eject an electron from a metallic surface, then electrons will always be ejected immediately after the light is turned on and the photons hit the metal.

(b)

The quantum confinement effect is observed when the size of the particle is too small to be comparable to the wavelength of the electron.To understand this effect we break the words like quantum and confinement, the word confinement means to confine the motion of randomly moving electron to restrict its motion in specific energy levels( discreteness) and quantum reflects the atomic realm of particles.So as the size of a particle decrease till we a reach a nano scale the decrease in confining dimension makes the energy levels discrete and this increases or widens up the band gap and ultimately the band gap energy also increases.

Implications of quantum confinement- energy levels become discrete.