Quantization of Energy

ABELLA / BASCUNA / RAVELO // IV - TRUTH

ULTRAVIOLET CATASTROPHE RAYLEIGH-JEANS LAW:

As l approaches zero, the function I approaches infinity.

Hence, according to classical theory, not only should short

wavelengths predominate in a blackbody spectrum, but also

the energy emitted by any black body should become

infinite in the limit of zero wavelength.

ULTRAVIOLET CATASTROPHE

In contrast to this prediction, the

experimental data plotted in Figure

40.5 show that as wavelength

approaches zero, intensity also

approaches zero. This mismatch of

theory and experiment was so

disconcerting that scientists called it

the ultraviolet catastrophe.

Note: This “catastrophe”— infinite energy—occurs as the

wavelength approaches zero; the word ultraviolet was

applied because ultraviolet wavelengths are short.

ULTRAVIOLET CATASTROPHE The Ultraviolet catastrophe is the error

at short wavelengths in the Rayleigh–

Jeans law known as the “classical

theory” for the energy emitted by an

ideal black-body. The error, much more

pronounced for short wavelengths, is

the difference between the blue curve

(Rayleigh–Jeans law) and the red curve

(Planck's law).

BASICALLY:

At long wavelengths, the Rayleigh–

Jeans law is in reasonable agreement

with experimental data, but at short

wavelengths, major disagreement is

apparent.

MAX PLANCK’S SOLUTION

Planck assumed the cavity radiation

came from atomic oscillators in the

cavity walls of a blackbody (a

hypothetical object capable of

absorbing all the electromagnetic

radiation falling on it).

MAX PLANCK’S SOLUTION

TWO MAJOR ASSUMPTIONS OF MAX PLANCK 1. The energy of an oscillator can have only certain discrete values

En

En = nhf n = positive number called quantum number f = frequency of the oscillator

h = Planck’s constant

Since energy can only have discrete values En, we say that energy

is quantized.

MAX PLANCK’S SOLUTION

TWO MAJOR ASSUMPTIONS OF MAX PLANCK 2. The oscillators emit or absorb energy when making a transition

from one quantum state to another.

The amount of energy emitted by the oscillator and carried by the

quantum of radiation is given by E = hf

An oscillator emits or absorbs energy only when it changes quantum states. If it remains in one quantum state, no energy is

absorbed or emitted.

MAX PLANCK’S SOLUTION This is an energy-level diagram

showing the quantized energy levels

and allowed transitions proposed by

Planck.

The major point of Planck’s theory is

the assumption of quantized energy

states which led to the birth of

quantum theory – a clear deviation

from the classical theory.

MAX PLANCK’S SOLUTION

HIGH FREQUENCIES (short WAVELENGTHS) LOW FREQUENCIES (HIGH WAVELENGTHS)

Energy levels are far apart Energy levels are close together

Large energy for each transition Small energy for each transition

Boltzmann factor is small Boltzmann factor is large

Relatively less energy states are excited Many energy states are excited

Large energy per transition but less excited states = low intensity

Many excited states but small energy per transition = low intensity

MAX PLANCK’S SOLUTION

Max Planck then generated a theoretical expression which

matched the experimental curve at all given wavelengths.

Planck’s constant (h) was derived experimentally. First he

assumed that light behaved like particles which had

energy hf with f as the frequency and h as the constant.

Then through experimentation using a vacuum tube. He

then excited electrons in the cathode with a lightsource of

known wavelength and measured the energy across the

tube. Given f and E he was able to derive the value for h.

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