# If an atom is in its ground state, has the atom the lower energy possible and there is its lower temperature?

"In the lowest energy state, the constituents of the atom (the nucleus and the orbiting electrons) are arranged so that the total energy in the system is minimal. This is called the ground state of the atom."

• has the atom the lower energy possible and is there just its lower temperature?
• it means, all atoms of the same type have the same ground state?
• It's by definition the lowest energy possible: "the total energy is minimal." – Gabriel Golfetti Aug 8 '18 at 17:04
• As for the other, not in general. We could degenerate ground states (distinct states with the same, minimum, energy). All the atoms of a certain species and isotope in the ground state will have to be in one of these states, however. – Gabriel Golfetti Aug 8 '18 at 17:06

## 1 Answer

The ground state of any given atom is, by definition, the single lowest-energy state possible with the atom. (On the other hand, it generally only refers to the internal degrees of freedom of the system, and it leaves the door open to center-of-mass motion. Strictly speaking, the absolute global ground state would require the center-of-mass motion to have zero kinetic energy and therefore exactly zero momentum so, at least in free space and in the absence of any trapping potentials, the Heisenberg uncertainty principle would require the atom to be delocalized over all space.)

Moreover, strictly speaking, the ground state of the atom is only possible at exactly zero temperature. If the atom is at any nonzero temperature (as required by the Third Law of thermodynamics) then its first excited state will be populated with a probability $$p \sim \exp\left(-\frac{\Delta E}{k_BT}\right),$$ where $\Delta E$ is the energy gap to the first excited state and $k_B$ is Boltzmann's constant. In practice, $\Delta E/k_B$ is generally of the order of $12,000\:\rm K$, and with respect to that energy scale, any temperature that's mildly cool by reasonably standards is effectively zero.

And, finally,

• all atoms of the same type have the same ground state?

Yes, all atoms of the same type have the same ground state (though it's unclear to me why you think that that is related to your initial question ─ it isn't, really).

• Sorry, of course, i did my question very quickly and , I want to say if several atoms are in the same ground state, so, are those atoms of the same type? and other question about of what you wrote, does ground state exist, if experimentally zero temperature haven't be possible ?, many thanks – PCat27 Aug 8 '18 at 23:51
• That makes less sense than before. – Emilio Pisanty Aug 9 '18 at 5:42
• As for your T=0 question, I should calculate the thermal excitation probability, say, at room temperature, for yourself. You can then decide whether that level of confidence is enough to say that the ground state has been achieved. – Emilio Pisanty Aug 9 '18 at 5:45