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Dr. Christopher S. Baird

How can an electron leap between atomic levels without passing through all the space in between?

Category: Physics      Published: June 18, 2014

electron transitions in hydrogen atom
Shown here are important electron transitions in the hydrogen atom. When an electron transitions between atomic states, it does not instantaneously leap. Public Domain Image, source: Christopher S. Baird.

An electron that is transitioning between two atomic states does not skip any intervening space. The idea of a quantum leap is highly misleading and commonly misunderstood. First of all, an electron is a quantum object. As such, it acts both as a wave and as a particle at the same time. When bound as part of an atom, an electron mostly acts like a wave. An atomic electron spreads out into cloud-like wave shapes called "orbitals". If you look closely at the various orbitals of an atom (for instance, the hydrogen atom), you see that they all overlap in space. Therefore, when an electron transitions from one atomic energy level to another energy level, it does not really go anywhere. It just changes shape. The orbital shapes with more fluctuations (with more highs, lows, and bends to its shape) contain more energy. In other words, when an electron transitions to a lower atomic energy level, its wave shape changes to have less kinks in it. But the electron does not "leap" anywhere.

The wave behavior of an electron in an atom is very similar to the behavior of classical waves on a guitar string. When you pluck a guitar string, you excite standing waves in the string, which are what make the sound. A certain string can only experience certain types of standing waves because the string is clamped down on both ends. The types of waves allowed on a particular string are called its "harmonics". The harmonics of a string depend on the string's length, tension, and mass density. A particular guitar string (of a particular length, tension, and mass) can therefore only play a certain type of sound, which is a combination of its harmonics.

If you are very careful about how you pluck the string, you can create a wave on the string which is mostly the lower, fundamental harmonic (which has very few kinks), or you can create a wave on the string which is mostly a higher harmonic (which has many kinks). It takes more energy and is therefore harder to strongly excite the higher harmonic in a guitar string. Furthermore, if you pluck the string properly so as to strongly excite a higher harmonic wave in the string, you can even coax the string to transition down to the lower-energy harmonic. The wave on the guitar string does not go anywhere when the string transitions from a higher-energy state to a lower-energy state. The wave just changes shape. In a similar way, the discrete set of electron orbitals possible in a certain atom are effectively the harmonics of the atom. The electron can transition to a higher harmonic wave shape by absorbing energy and kinking more, or transition to a lower harmonic wave shape by emitting energy and kinking less (relaxing).

It should be clear at this point that an electron that transitions in an atom does not make any kind of leap from one location in space to another location in space. But you may still be worried that the electron makes a leap from one energy level to another, and therefore bypasses all the in-between energy states. Although we are talking about a leap on the energy scale, and not a leap in space, such a leap may still strike you as unnatural, as it should. The fact is that an electron transitioning in an atom does not actually discontinuously leap from one energy level to another energy level, but makes a smooth transition. You may wonder, "Doesn't quantum theory tell us that an electron in an atom can only exist at certain, discrete energy levels?" Actually, no. Quantum theory tells us that an electron with a stationary energy can only exist at certain, discrete energy levels. This distinction is very important. By "stationary energy" we mean that the electron's energy stays constant for a fairly long period of time. The orbitals of a particular atom are not the only allowed states that an electron can take on in the atom. They are the only stable states of the atom, meaning that when an electron settles down to a particular state in an atom, it must be in one of the orbital states.

When an electron is in the process of transitioning between stable states, it is not itself stable and therefore has less restrictions on its energy. In fact, an electron that transitions does not even have a well-defined energy. Innate quantum uncertainty arises in the electron's energy because of its transition. The quicker an electron transitions, the more uncertain its energy. This "innate quantum uncertainty" is not some metaphysical mystery, but is better understood as the wave spreading out over many values. Just as the electron can spread out into a wave that extends over a region of space, it can also spread out into a wave that extends over a region along the energy scale. If you calculate the average energy (the "expectation value") of this transitioning electron's spread of energies, you find that the electron's average energy does not instantaneously jump from one energy level to another. Rather, it smoothly transitions on average from the one energy level to the other energy level over a period of time. There is really no "instantaneous quantum leap" at all. The electron does not leap in space, and it does not leap up the energy scale. In fact, the term "quantum leap" is almost universally shunned by scientists as it is highly misleading. If you want a better mental image, you can think of the electron as quickly, but smoothly sliding along the energy scale from one stable state to the next. Because a typical atomic electron transition is so fast (often on the order of nanoseconds), it can seem to be nearly instantaneous to the slow human senses, but fundamentally it is not.

Topics: atom, atoms, electron, electron transition, quantum, quantum leap, transition, wavefunction