The Bohr's postulate states that an electron does not emit energy when it is in a stationary state. My question is, is it only a postulate or does it have proof? Also on what basis did Bohr come to this conclusion that there are stationary states where an electron does not emit energy?

# [Physics] Why does an electron not emit energy when it is in a stationary state

accelerationatomic-physicselectromagnetismelectronsorbitals

#### Related Solutions

Why do electrons in an atom occupy only the stationary states?

This isn't true. An electron in an atom can be in any superposition of states. This is one of the basic postulates of quantum mechanics: linearity.

For example, say an atom has a ground state 1 and an excited state 2, and let's say we're able to prepare it in a pure state 2. It will decay electromagnetically to state 1. This decay is represented mathematically by a process in which the wavefunction becomes a mixture of states 1 and 2, with the amplitude of 2 decaying exponentially and the amplitude of 1 growing correspondingly.

Energy is special here only because many of the measuring devices we use to study atoms are energy-sensing devices. When we measure using one of these devices, we always get a definite energy. Take the two-state example again for simplicity. In the Copenhagen interpretation (CI), this is because of wavefunction collapse. In the many-worlds interpretation (MWI), the measuring device becomes a superposition, but it's a superposition of a state in which the device measured a single energy and another state in which the device measured the other energy. You can also discuss this in terms of decoherence.

Electron as a standing wave

Yes, the electron is a standing wave. See atomic orbitals on Wikipedia: *"The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves"*.

I couldn't understand how come Bohr who interpreted electron as a particle, formulated an equation for electron's angular momentum which shows its mathematical proof to be a wave.

Maybe you need to check out De Broglie and matter waves: *"All matter can exhibit wave-like behaviour. For example a beam of electrons can be diffracted just like a beam of light or a water wave".* See this picture by artist Kenneth Snelson:

It isn't a totally accurate depiction. Electrons aren't actually thin coloured strips, but you should get the idea of these standing waves.

Simply when one compares first harmonic of wave on a string with electron moving around nucleus, from where the nodes shown in the figure arise in case of orbiting electron?

It's bit like a wave in a closed string. But it isn't a wave on a string, it's an electromagnetic wave that's configured as a standing wave. A field variation that's configured as a standing field. It has a Compton wavelength of 2.426 x 10⁻¹² m.

The electrons can only orbit stably, without radiating

Don't think of the electron as some little billiard-ball thing. Think of it as something more like a hula hoop.

So as we move towards some nth harmonic, the trajectory becomes complicated. Is it that case?

Yes. Check out spherical harmonics.

Also that how s,p,d, and f orbitals (May be, the way in which electron, a wave, moves around nucleus as a function of time taken?) do exist without interfering each other? I mean, an atom is so small and intact.. So, don't they mix up i.e., superpose?

Superposition is a wave thing. Two ocean waves can ride right over one another and then keep going. But for electrons in orbitals, like Acid Jazz said, the Pauli Exclusion principle applies. The simplest analogy I can think of for that is *two whirlpools can't overlap*.

## Best Answer

To begin with, I would suggest not to attach too much importance to Bohr's approach. It had the great merit of suggesting a novel idea and to give the first explanation to a great problem: the one of atomic spectra, as explained by anna v. And it was not a vague idea: his formula for the energy of hydrogen levels $$E_n = -{m\,e^4 \over 2\,\hbar^2 n^2}$$ (Gauss units) fitted experimental data up to at least 6 significant digits, as far as I can remember. It should also be remarked that Bohr's formula is made entirely of known fundamental constants: there was no room for adjustable parameters, either it fitted or not. It did.

But it never grew to a real theory, and its "old quantum mechanics" was short lived: from 1913 to 1925 at most.

Bohr's idea of stationary states was necessary to overcome the absurdity following from Rutherford's planetary model together with classical electromagnetism: if both were true, atoms would not exist. Bohr was the first to know that his postulate was inconsistent with Maxwell's electromagnetism - which is the basis, I suppose, of your question.

However the concept of stationary state survived old q.m. and passed to the "new" q.m. founded by Heisenberg and Schrödinger (not forgetting de Broglie's suggestion of waves associated to particles: his famous $\lambda=h/p$). But here some clarification is in point.

First, as far as experimental facts are concerned, each atom has only

onestationary state: its ground state, i.e. the one of the least energy. If you push the atom, in any way, to an excited state, it sooner or later decays, emitting one ore more photons. But what does theory say?If Schrödinger equation is applied to hydrogen atom it gives an infinity of stationary states, with energies exactly given by Bohr's formula. And according to q.m. these are

truestationary states, i.e. states which do not evolve in time, remaining the same forever. But this is patently wrong, given the experimental facts. Energies are right, as is proven by measured energies of photons emitted or absorbed by the atom. But Schrödinger's stationary states do not exist in nature, other than as an approximate description of what are only transient states (with the only exception of the ground state).Actually theory was soon able to do a step forward. If an electromagnetic wave hits an atom, calculations show that two things can happen, according to the initial state of the atom and the frequency of the wave:

absorption.stimulated emission.In both cases there is a relation between the atom's energy change and the wave's frequency. It is the second famous Bohr's formula: $$|\Delta E| = h\nu.$$

It is almost certain that whoever read this formula thought of photons - and this is right, as Bohr himself deduced the formula thinking of photons. But it is important to note that the theory I alluded above knows of no photons: it is, in physicists jargon, a

semi-classical theory. This means that electromagnetic field is treated following Maxwell, whereas the atom is a Schrödinger atom.So far so good, but what about

spontaneousemission? It exists, as is proven by experimental facts (an excited state spontaneously decays via photon emission). Yet semi-classical theory is unable to deal with it. There was however another seminal paper by Einstein (1917) where he showed on general grounds that all three processes must exist (absorption, stimulated emission, spontaneous emission) and gave simple formulas relating the rates of those processes. But a theory of spontaneous emission had to wait for the birth of QED (quantum electrodynamics). In this theory electromagnetic field is treated according the prescriptions of quantum mechanics and its quanta - photons - naturally arise.Needless to say, QED calculations exactly reproduce Einstein's predictions about the ratios between rates of photon emission and absorption.