# Do hydrogen atoms continuously emit radiation?

1. Feb 7, 2005

### what_are_electrons

Three (3) Questions:

1. Keeping in mind the light emitted by Synchrotrons, then taking the electron as a point charge, and assuming that it orbits the proton in accord with a proper 1s type wave function, does that electron continuously emit (and/or absorb) radiation other than virtual pairs even if it is for time < 10(-18) sec?

2. If it does emit radiation, then what energy level, if any?

3. If so, from where does the atom get the energy to maintain that quantum state?

2. Feb 7, 2005

### masudr

1. If an electron is in the ground state (i.e. energy eigenstate corresponding to the lowest allowed energy level = 1s) it will not emit any energy. Realise that the electrons aren't orbiting the nucleus in any classical sense.

2. See above. Also, the radiation doesn't have an "energy level". Energy levels are different energies corresponding to some energy eigenstate, usually in an atom.

3. See answer 1, the electron does not emit any energy. You must realise that the classical equations do not apply.

3. Feb 7, 2005

### dextercioby

At the most elementary level (assumed by Schrödinger's equation),the total energy of the atom is composed by the KE from the electron(s) and nucleus + the electrostatic Coulomb attraction+repulsion terms...

Daniel.

4. Feb 7, 2005

### what_are_electrons

Electrons undergoing acceleration emit radiation in a synchrotron. Right? Does the electron in the hydrogen atom undergo acceleration or not? If it is being accelerated continuously, then why doesn't it emit radiation?

5. Feb 7, 2005

### dextercioby

Yes.

No.Acceleration is a classical concept.It does not pertain to the quantum world,hence cannot be used in the (quantum mechanical) description of matter.

Because the energy levels are quantized...??

Daniel.

6. Feb 7, 2005

### what_are_electrons

OK. Then I should understand that the light emission by the electrons in the synchrotron is best described by QM. If so, please elaborate a bit. Thanks.

7. Feb 7, 2005

### dextercioby

Synchrotron radiation is described with satisfactory results both at classical level (relativistic CED) and at quantum level (QED,not QM).The differences are fundamental and come from the classical,respectively quantum description of both the particles accelerated and of light.

This is the simplest picture it can be given under these circumstances.

Jackson's book and a book on QED (e.g.Ahiezer & Berestetzkyy,Jauch & Rohrlich) could provide the necessary (mathematical) details and the physical interpretation of results.

Daniel.

8. Feb 8, 2005

### Aki

I thought everything, hot or cold, emits radiation.

9. Feb 8, 2005

### dextercioby

I know what u're referring to,but the discussion was around quantized energy levels of atoms and the electrons being in pure stationary states in which they do not emit any radiation (classical or quantized) whatsoever.Atoms are neither cold,nor hot...

Daniel.

10. Feb 8, 2005

### Staff: Mentor

In QM, we usually make the connection with classical physics by way of expectation values of physical quantities. When the electron is in one of hydrogen's "energy levels," it is in what we call a stationary state, in which the probability distribution of the electron's position does not change with time. This means that the expectation value of position, <x>, does not change with time. In that sense, we can say that an electron in a particular energy level is not in fact accelerating.

To carry this interpretation further, when an electron is in the process of making a transition from one energy level to another, its Schrödinger wave function can be represented as a linear combination of the wave functions for the initlal and final states:

$$\Psi = a \Psi_{initial} + b \Psi_{final}$$

where a and b vary with time so that before the transition begins a = 1 and b = 0, and after the transition ends a = 0 and b = 1. It turns out that <x> is not stationary for this wave function; it oscillates in time, with a frequency that is equal to the frequency of the light emitted in the transition! In this case we can consider the electron to be accelerating, and emitting radiation as a result.

11. Feb 8, 2005

### Chronos

Atoms do not radiate intrinsically. If they did, they would lose mass and evaporate. They do, however, reradiate energy they absorb from their surroundings. Since the CMB temperature is presently 2.7K, there is still enough free energy to power this effect.

12. Feb 8, 2005

### marlon

Electrons are bound to the atomic nucleus by a Coulombic potential. Some people think that due to this Coulombic interaction, the electrons are accelerated and therefore they must radiate continuously. This is wrong (the radiation part that is) because the orbitals (the regions where you can find a certain electron at a certain energy-state) are stable. To see this, just imagine this: when an electron is close to the nucleus, the Coulombic interaction is stronger, yielding a potential energy that is smaller (more negative). However, the kinetic energy of such electrons is bigger. So electrons that are close to the nucleus have a lower potential energy but they move faster in the orbitals, yielding a higher kinetic energy. When looking at electrons that are firther away from the nucleus, the potential energy rises and the kinetic energy lowers. In the end, these two effects of energy will yield a stable situation. Therefore, there will be no radiation.

regards
marlon

13. Feb 8, 2005

### marlon

this is due to the equilibrium in energy of the electrons. read the example of my above post.

marlon

14. Feb 8, 2005

### masudr

To rescue atoms continuously emitting radiation we had to invent a whole new theory of the universe. This was one of the greatest motivations for QM!

15. Feb 8, 2005

### Edgardo

If the electron orbited the proton, then yes, it would emit radiation
because an accelerated charge emits radiation. But that would also mean it loses energy, namely kinetic energy. What happens?
Well, the electron would crash into the proton and hydrogen wouldn't exist (hmm...
what's actually so bad about an electron crashing into the nucleus, lol. Why's there
no hydrogen where the electron is sticked together with the nucleus?)

That's why the 'planet model' isn't really good.
My teacher once said: 'You shall not make for yourself a carved image of the atom'
(one of the ten commandments).

Unfortunately that implies that you can't really say what an atom looks like.

16. Feb 8, 2005

### what_are_electrons

Does this mean that electrons that are linearly or circularly accelerated (like at SLAC or CERN or KEK etc.) can not be described with QM?

17. Feb 8, 2005

### dextercioby

They can,but the theory which does,if it's a quantum theory (it may not be,it may simply be SR),will not use the word and the concept "acceleration".

Daniel.

18. Feb 8, 2005

### what_are_electrons

At RT most atoms on the earth have kT of energy, about 0.025 eV. Would all atoms have that energy available for use? Is that more than the microwave BG?

19. Feb 8, 2005

### what_are_electrons

This seems to contradict XPS results that show that the 1s electron clearly has the largest BE (in effect PE), The heaviest atoms have 1s BE >90,000 eV. All other electrons have lower BE as their radius increases.

20. Feb 8, 2005

### dextercioby

Your whole previous post denotes not knowing the basic Bohr model of (H) atom,not to mention the QM model.