[chris (OP)]

Gerald has written to ask:

Generally the temperature is an indicator for the speed of atoms a matter.  Given the fact that all atoms of all matter has no speed at 0K (-273°C) my question is:

Do all atoms at a precise temperature (say 30°C ) have the same speed, no matter the material or state?
So, e.g. I have a glass of water with a spoon inside on my kitchen table, all by 30°C as normal here in Panama
Have the atoms or molecules in the water the same speed as the air molecules around the glass, or the atoms in the grid of the metal of the spoon or in the crystal grid of the glass?

Greetings from (high temperature) Panama
Gerald

What does everyone think?

[evan_au]

Do all atoms at a precise temperature (say 30°C ) have the same speed, no matter the material?

No.
- The velocity of an individual atom at a given instant is random, from zero to around the speed of sound in that material.
- More massive atoms move more slowly, on average

However, the average velocity of a large group of atoms is determined by the temperature.
 
It is possible to make a more general statement than one just about speed when you have an ideal gas: The average energy of a group of atoms increases proportionally with temperature. Kinetic energy E=1/2mv² = kT.
- where:
- E is Energy in Joules
- m is the mass in kilograms
- v is the velocity in meters/second
-  temperature T is measured in degrees Kelvin
- k is the Boltzman constant

This means that if you have different atoms (or different isotopes), the average speed increases:
- As the square root of absolute temperature
- As the inverse square root of the atomic mass

no matter the ...state?

When materials change state (eg between solid and liquid, or liquid and gas), the velocity of the particles can change without a change of temperature.

See: https://en.wikipedia.org/wiki/Thermal_energy#Relation_to_heat_and_internal_energy

[chiralSPO]

It is possible to make a more general statement than one just about speed when you have an ideal gas: The average energy of a group of atoms increases proportionally with temperature. Kinetic energy E=1/2mv² = kT.
- where:
- E is Energy in Joules
- m is the mass in kilograms
- v is the velocity in meters/second
-  temperature T is measured in degrees Kelvin
- k is the Boltzman constant

This means that if you have different atoms (or different isotopes), the average speed increases:
- As the square root of absolute temperature
- As the inverse square root of the atomic mass

This is a great answer, and I would like to add to it.

The ideal gas approximation is an excellent way to answer the OP for monoatomic gases (He, Ne, Ar, etc.), but since the OP specifically asks about atomic motion, I would like to add that for polyatomic molecules (especially for gas and liquid states), there are also internal motions--the atoms within a molecule are in constant motion, vibrating and rotating and boggling frequencies (even at 0 K, look up "zero point energy" to learn more about that). These internal motions are largely responsible for differences in heat capacity* between substances.


* I mean molar heat capacity. Specific heat values are dominated by molar mass.

[PmbPhy]

Gerald has written to ask:

Generally the temperature is an indicator for the speed of atoms a matter.  Given the fact that all atoms of all matter has no speed at 0K (-273°C) my question is:

Do all atoms at a precise temperature (say 30°C ) have the same speed, no matter the material or state?...

No. The kinetic energy of the atoms vary according to the Boltzmann distribution. For details please see:
https://en.wikipedia.org/wiki/Boltzmann_distribution