Planck's Quantum Theory — Overview & Planck's Constant

$$\Large\color{#D73D75}{Planck's\ Contributions\ To\ Chemistry}$$

Background On Blackbody Radiation

Blackbody radiation occurs when a heated solid object glows. You might have noticed this with the coils on an electric stove. As the metal is heated, it gives off a red-orange glow.

Scientists investigated the wavelengths of light emitted by blackbody radiation. They found that the wavelengths varied based on how much heat is applied. Initially, solid metal objects would glow red, then orange, and finally white with increasing heat. Red light has longer wavelengths and lower energy than white light. Scientists hypothesized that with continued heating, the emitted wavelengths would enter the ultraviolet region and the intensity would increase infinitely. This did not occur! It was discovered that the light emitted would reach a maximum wavelength and the intensity drops drastically.

Planck and Quantized Energy

Max Planck was able to explain the phenomenon of blackbody radiation not rising continuously. Planck stated that energy emitted by an object was not continuous and indefinite. In fact, energy can only be emitted in definite amounts or quanta.

Energy is defined as quantized meaning that it changes by definite amounts. Think about climbing a ladder versus a ramp. On a ramp the change is continuous from start to end. A ladder must be climbed one rung at a time, you cannot step in-between rungs.

Planck's Constant

The energy of radiation can be described with the equation:

$$E=h\nu\\ \textbf{or}$$ $$E=\frac{hc}{\lambda}\\ where,\ \nu=\frac{c}{\lambda}$$

The amount of energy ($E$) is affected by the frequncy of the radiation $(\nu)$. Planck's constant is represented by $h$ where $h=6.626\times10^{-34}J\ \cdot\ s$. This constant relates light or a photon's energy to the frequency. The constant $c$ is the speed of light and $c= 2.99792458 \times 10^8 m/s$.

For example, the energy of blue light at 450nm can be calculated.

$$E=\frac{(6.626\times10^{-34}J\ \cdot\ s)(2.99792458 \times 10^8 m/s)}{4.50 \times 10^{-7}m}\\$$ $$=4.41 \times 10^{-19} J$$

Planck's Quantum Theory

(Video) Postulates of Planck's Quantum Theory | Class 11 Chemistry |Black body radiation | Atomic Structure

by: Digital Kemistry

This video goes over and explains the different parts of Planck's Quantum Theory (such as the the idea that energy is quantized and how energy is not continuous). This video also defines photons and how they related to Planck's Quantum Theory. This video also explains Planck's equation and the derivation of Plank's equation.

We're beginning our study of quantum mechanics. Quantum mechanics explains the behavior of electrons. Why do we care? In chemistry, it helps to explain bonding. We want to know how atoms interact to form covalent and ionic bonds. Eventually, we'll understand different models of how atoms bond. For example, we'll look at the valence bond theory and the molecular orbital theory. But, for now, we need to build the foundation. Let's explore how scientists began to rethink their understanding of the laws of physics.

Science in 1900

At this point in history, many chemists and physicists thought our understanding of the universe was almost complete. We were incredibly familiar with Newton's laws and electromagnetism. And we were continually using them to develop and adapt new technologies. But, there were a few outstanding problems that we needed to solve. One of those problems was blackbody radiation.

You've probably seen this phenomenon before. If you have an electric stove, the coils glow as they heat up. We manufacture stove coils by alloying the transition metals nickel and chromium. Remember alloying improves the chemical and physical properties. So, it's unbelievably strong! Its melting point is $1400.0^{o}C$! So, we can heat it to a very high temperature, and it will remain solid. But what happens as it's heated? At first, it begins to glow orange-red. Then, eventually, it will glow white.

So, what is a black body? Technically, a black body is an object that absorbs all wavelengths of electromagnetic radiation. We can also think of it as emitting all wavelengths of light. However, the intensity and peak wavelength depends on the temperature. Most room temperature objects peak in the infrared region and have minimal intensity. We can't see that. But, as the temperature increases, the peak shifts to the visible region. The intensity also increases dramatically. That's why we see the red glow of the stove coil. What about at high temperatures? The peak shifts into the ultraviolet region.

But what was the problem? Classical electromagnetism predicted a black body would emit at an infinite intensity in the ultraviolet region. That disobeys the first law of thermodynamics! Why? A black body could produce an unlimited amount of energy. Thankfully, everyone recognized that it was a problem. It didn't match our understanding of thermodynamics. Moreso, it didn't fit the experimental data. The experimental data showed that the intensity drops to zero as the wavelength decreases. But no one understood why!

Quantization of Energy

In 1901, Max Planck solved the problem. He proposed that energy was quantized. What does that mean? The emitted energy is restricted to specific values. To help us understand, let's consider the atomic scale. Heat is the transfer of kinetic energy between atoms and molecules. So, as we heat a black body, the atoms have more kinetic energy. So, what's happening in our stove coil? Metals experience metallic bonding. So, the atoms form a lattice structure. That limits the variety of movements they have. In a crystal lattice, the atoms can only oscillate. But, the metal also has a sea of electrons. The electrons also oscillate as they gain energy. What happens when charged particles oscillate? They produce electromagnetic waves. That's a fancy way of saying they emit light!

But where does quantization occur? At the quantum scale, most things are quantized. So, the oscillations of the atoms and electrons are quantized. The promotion of electrons to higher energy levels is also quantized. The rotations of a molecule are quantized. A black body has various methods of gaining and losing energy. Some are beyond my explanation above. But, oscillating electrons are the main method. The key concept is that they only occur in set amounts. For an electron to reach a higher energy level it must absorb a specific amount (quanta) of energy. It cannot absorb more or less. To return to the lower energy state, it emits light. The ultraviolet region is at a high energy level. So, it's unlikely that many electrons will reach the correct energy state. In the classical model, scientists assumed all energy states were equally likely. Planck realized that the high-energy states have a significantly lower probability. Why? Because they would have to absorb the exact right amount of energy. And that amount is much larger than the visible or infrared regions.

From Planck's concept, we can determine the equation $E=nh\nu$.

• $E$ is the energy of the emitted light. In a blackbody, the light's energy equals the energy lost by an electron as it relaxes.

• n is a whole-number integer (0, 1, 2, 3, etc.) that creates the quantization.

• h is Planck's constant with a value of $6.626\times10^{-34}\frac{J}{s}$.

• $\nu$ is the frequency of the light.

What does this equation tell us? At a specific frequency, matter can only emit and absorb energy in whole-number ratios. The ratio is determined by the $n$ value and Planck's constant. Notice that Planck's constant is tiny! The scientific notation is $10^{-34}$. That explains why we don't perceive quantization at the macroscale. The boundaries are too small except at the atomic and subatomic scales. This solved the black body radiation problem because $n$ could equal zero. So, a blackbody can have high frequencies but low intensities in the ultraviolet region.

(Video) What is a Black Body & Black Body Radiation

by Physics Made Easy

These two videos will help you to better understand the background behind Planck's Quantum Theory. Planck was trying to solve problems created by Black Bodies and Black Body radiation. The first video defines and illustrates black bodies. The second video investigates black body radiation.