*This is the second in a series of articles exploring the birth of quantum physics.*

Word *quantum* is everywhere, and with it the term *quantum leaps*. Last week we discussed Max Planck’s pioneering idea that atoms could emit and absorb energy in discrete amounts, always multiples of the same amount. These small pieces of radiation have been given the name of quantum.

This week, we move on to another key idea of the quantum revolution: Niels Bohr’s atomic model of 1913, which gave us quantum leaps. If Planck’s idea required courage and a lot of imagination, Bohr’s was a huge feat of bravado. Somehow Bohr bagged a bunch of new ideas, mixed them with old concepts from classical physics, and came up with the notion of quantized orbits in atoms. Let the model held look simply amazing. Bohr saw what no one could see at the time: that atoms are nothing as people had thought for at least 2,000 years. In fact, they are unlike anything anyone could have imagined. Except Bohr, I guess.

## A revolution of the simplest particle

Bohr’s atomic model is a little crazy. His collage of ideas mixing old and new concepts is the result of Bohr’s incredible intuition. Looking only at hydrogen, the simplest of all atoms, Bohr formed the image of a miniature solar system, with a proton in the center and the electron surrounding it.

Following the physicist’s way, he wanted to explain some of his observed data with the simplest possible model. But there was a problem. The electron, being negatively charged, is attracted to the proton, which is positive. According to classical electromagnetism, the theory that describes how charged particles attract and repel each other, an electron spirals down toward the nucleus. As it circles the proton, it would radiate its energy and fall. No orbit would be stable and atoms could not exist. Obviously, something new and revolutionary was needed. The solar system could not go as far as analogy.

To save the atom, Bohr had to invent new rules that clashed with classical physics. He bravely suggested the implausible: what if the electron could only go around the nucleus in certain orbits, separated from each other in space like the steps of a ladder or the layers of an onion? Just as you cannot stand between two steps, the electron cannot stay anywhere between two orbits. It can only jump from orbit to orbit, the same way we can jump between stages. Bohr had just described quantum leaps.

## Quantified momentum

But how are these quantum orbits determined? Once again, we will bow to Bohr’s incredible intuition. But first, a foray into angular momentum.

If electrons spin around protons, they have what we call angular momentum, a quantity that measures the intensity and direction of circular motions. If you tie a stone to a rope and spin it, it will have an angular momentum: the faster you spin, the longer the rope or the heavier the stone, the greater this moment. If nothing changes in the rotational speed or the length of the string, the angular momentum is conserved. In practice, it is never preserved for rotating rocks because of friction. When a swirling ice skater spins by bringing her outstretched arms to her chest, she is using her nearly conserved angular momentum: shorter arms and more spin yield the same angular momentum as longer arms and slower spin.

Bohr suggested that the angular momentum of the electron should be quantized. In other words, it should have only certain values, given by integers (n = 1, 2, 3…). If L is the orbital angular momentum of the electron, Bohr’s formula reads, L = nh/2π, where h is Planck’s famous constant that we explained in last week’s essay. A quantized angular momentum means that the orbits of the electron are separated in space like the steps of a ladder. The electron could jump from one orbit (say the n=2 orbit) to another (say n=3) either by jumping down and closer to the proton, or by jumping up and further away.

## Colored quantum fingerprints

Bohr’s brilliant combination of concepts from classical physics with brand new quantum physics produced a hybrid model of the atom. The world of the infinitely small, he realized, demanded a new way of thinking about matter and its properties.

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In the process, Bohr solved an old mystery in physics regarding the colors a chemical element emits when heated, known as the emission spectrum. The intense yellow of sodium lamps is a familiar example of the dominant color in an emission spectrum. It turns out that each chemical element, from hydrogen to uranium, has its own spectrum, characterized by a distinctive set of colors. These are the spectral fingerprints of an element. The scientists of the 19^{e} century knew that chemical spectra existed, but no one knew why. Bohr suggested that when an electron jumps between orbits it emits or absorbs a chunk of light. These quantities of light are called *photons*and they are Einstein’s key contribution to quantum physics – a contribution we will explore soon in this series.

Since the negative electron is attracted to the positive nucleus, it needs energy to jump to a higher orbit. This energy is acquired by absorbing a photon. It is the basis of the *absorption spectrum*, and you do the same every time you climb a step on a ladder. Gravity wants to hold you down, but you use the energy stored in your muscles to move you up.

On the other hand, the emission spectrum of an element consists of the photons (or radiation) that electrons emit when they jump from higher orbits to lower orbits. The photons take away the angular momentum that the electron loses by jumping down. Bohr suggested that the energy of the emitted photons corresponds to the energy difference between the two orbits.

And why do different elements have different emission spectra? Each atom has a unique number of protons in its nucleus, so its electrons are attracted to specific intensities. Each orbit allowed for each atom will have its own specific energy. When the electron jumps between two orbits, the emitted photon will have that precise energy and no other. Returning to the ladder analogy, it’s as if each chemical element had its own ladder, with steps built at different distances from each other.

With this, Bohr explained the emission spectrum of hydrogen, a triumph of his hybrid model. And what happens when the electron is at the lowest level, n=1? Well, Bohr suggests it’s as low as possible. He doesn’t know how, but the electron is stuck there. It does not crash into the core. His student, Werner Heisenberg, gave the answer some 13 years later: the uncertainty principle. But that’s a story for another week.

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