Quantum Mechanics: Motions and the Scale of Quantum Jumps


By Robert M. Hazen, Ph.D.George Mason University

The study of motions at the scale of quantum jumps is called quantum mechanics. Things that happen all around at everyday speeds, at everyday masses, and at everyday scales may not be at all relevant at the atomic scale, and so physicists of the early-20th century had to keep an open mind.

Artistic render of electrons orbiting around the nucleus on the cosmic background.
According to quantum mechanics, every measurable quantity comes in discrete bundles. (Image: Jurik Peter/Shutterstock)

Max Planck and the Concept of Quantum Mechanics

The first odd fact people have to accept about the universe at the atomic scale is that every measurable quantity comes in discrete units, bundles called quanta. The idea of the quanta was first proposed by the German physicist Max Planck, who lived from 1858 to 1947.

Planck’s career exemplifies and reflects this phenomenal transition in physics from the realm of classical physics of the late-10th century to modern physics of the early-20th century. 

He began his work squarely in the realm of classical physics. He studied electricity, magnetism, and thermodynamics. But by the early-20th century, he had defined the core principle of quantum mechanics, and he basically defined a whole new way of describing the physical world. By his mid-20s, Planck had received a professorship at the University of Kiel, where he offered a variety of advanced courses. 

In other words, he applied his mathematical abilities to theoretical physics. At that time, theoretical physics was considered a second-rate science. It was really marginalized, despite the important contributions it was making. It’s been suggested by some historians of science that this is because the field was dominated by Jewish mathematicians.

This is a transcript from the video series The Joy of ScienceWatch it now, on Wondrium.

How Classical Theory Deals with Energy

Planck’s piece of research on the photoelectric effect that culminated in 1900 was an extremely important piece of work. Planck began this work to explain the spectrum of electromagnetic radiation that was emitted from what’s called a ‘black body’. An ideal black body absorbs all electromagnetic radiation. 

A statue of Max Planck in Berlin.
Max Planck proposed the idea of quanta for the first time. (Image: Kiev.Victor/Shutterstock)

But the laws of thermodynamics require that energy be re-radiated out into the surroundings because there has to be a conservation of energy. It was the spectrum of this radiation that concerned physicists in the late-19th century. Classical theory, which deals with energy as a continuum, can’t explain the observed spectrum. It drastically overestimates the amount of energy that would be radiated at very short wavelengths. 

So shorter and shorter wavelengths mean higher and higher energies. And even though the total amount of radiation in those shorter wavelengths was less, that would be much more energy coming out of the black body than was going into it. And yet, the classical theory seemed to suggest that there should be a lot of these higher energy types of wavelengths. 

How Planck Solved the Problem of Classical Theory

To solve the problem, Planck suggested that energy comes in discontinuous steps or quanta. Now, this is some decades before Niels Bohr and his model of the atom. So this is the first idea about energy coming in discrete steps. The energy corresponds to different wavelengths, discrete frequencies of electromagnetic radiation. 

The energy carried by one electromagnetic wave is given by the wave’s frequency times a constant. And that constant is now known as Planck’s constant. So the equation is energy equals h—Planck’s constant—times nu, or the frequency. With this formulation, Planck was able to match the observed black body behavior of all sorts of objects for the first time, but it required that very bizarre assumption of quantized energy, quantized wavelengths. 

Few physicists of the time were ready to accept this strange and abstract idea. After all, energy in everyday situations occurs in a continuum, not in discrete steps. In other words, it doesn’t occur in quantum.

Learn more about the quantum world.

Albert Einstein’s Paper on the Photoelectric Effect

A portrait of Albert Einstein.
Albert Einstein reinforced Max Planck’s ideas on quantum in one of his four papers of 1905. (Image: Oren Jack Turner/Public domain)

Albert Einstein was able to reinforce Planck’s position. This was in 1905, in one of those four great papers that Einstein published in that year. This was a paper on the photoelectric effect by which light can eject electrons from certain materials. This is the effect that’s used in batteries and solar batteries.

It’s also used in solar panels. Sometimes photovoltaic materials come in little panels; sometimes, they come in very large ones. They are located on the tops of houses or by the sides of roads where there is solar energy. And what happens is this: a photoelectric material absorbs a photon, and that actually knocks an electron out of the material so it can flow as an electric current. 

If someone shines a bright light on a photoelectric material, electrons are ejected, and they become an electric current, in effect. What’s strange is that the velocities of these ejected electrons are independent of the light’s intensity. Force equals mass times acceleration, so if the oppressed force is increased on something, the acceleration is also increased. 

Learn more about the periodic table of elements.

Relationship between Light Intensity and Electron Velocity

So the idea of more light intensity giving electrons a higher velocity coming out is not true. When the intensity of light shining on a photovoltaic is increased, the velocity of the electrons stays exactly the same; just the number of electrons increases. But velocities do increase if one uses shorter wavelengths. 

For example, blue light has a shorter wavelength and more energy than red light, and the velocity of the electrons increases according to blue light. So it’s the energy of the wavelength—not the intensity of the light—that determines the velocity of the electrons that are kicked out of that photovoltaic. 

Einstein adopted Planck’s postulate, that is, that light waves carry energy, h times nu. And he showed that the kinetic energy of the electrons matched exactly the Planck energy that’s contained in the light.

Common Questions about Motions and the Scale of Quantum Jumps

Q: Who was Max Planck?

Max Planck was a German physicist and mathematician who first explored the idea of ​​quanta. He made a major breakthrough in classical physics and explained the laws of quantum mechanics in the early-20th century.

Q: How did Max Planck solve the problem of classical theory about continuum energy?

Max Planck used quantum mechanics to solve the problem of classical theory dealing with energy as a continuum. Accordingly, he stated that energy flows discontinuously and in discrete steps.

Q: How does a photoelectric material work to produce electric current?

When a photoelectric material absorbs photons, it emits an electron, generating an electric current. According to quantum mechanics, shorter wavelengths increase the velocity of electrons, and that leads to more electric current.

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