Rms speed of molecule vs atom

In summary, the problem involves finding the new pressure after adding heat to a helium atom until its rms speed has increased by 50%. The formula for rms speed is given, as well as the mass of a helium molecule. There is a question about whether the rms speed of a helium molecule is the same as that of an atom, and it is determined that since helium is a monatomic gas, the rms speed of the atom and the molecule would be the same.
  • #1
barrylwires
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Homework Statement


Heat is added until the rms speed of a helium atom has increased 50%. Find new pressure. (Not all parameters given.)


Homework Equations


rms = (3kT/m)1/2
mass of molecule = mass of mole/NA
Then, mass of helium molecule is 6.6x10-26kg

The Attempt at a Solution


Question: Is rms speed of a helium molecule the same as the rms speed of an atom. Yes, because the atoms make up the molecule? No, helium is diatomic (right?) and so that has to be taken into account??
 
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  • #3


The rms speed of a molecule and an atom are not necessarily the same. While both are affected by temperature and mass, the rms speed of a molecule also takes into account the molecular structure and the distribution of velocities of the individual atoms within the molecule. In the case of helium, which is a diatomic molecule, the rms speed would be slightly different from that of a single helium atom due to the presence of the two atoms and their interactions. Therefore, it is important to consider the specific properties of the substance when calculating the rms speed.
 

1. What is the difference between the RMS speed of a molecule and an atom?

The RMS (root mean square) speed of a molecule and an atom refers to the average speed of the particles within a gas. The main difference is that molecules are composed of multiple atoms, so their RMS speed takes into account the movement of all the atoms within the molecule.

2. How is the RMS speed of a molecule or atom calculated?

The RMS speed is calculated using the ideal gas law, which takes into account the temperature, mass, and molar mass of the gas particles. The formula is: RMS speed = √(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.

3. Does the size of a molecule or atom affect its RMS speed?

Yes, the size of a molecule or atom does affect its RMS speed. Generally, larger molecules or atoms have a lower RMS speed compared to smaller ones, as they have a larger mass and therefore require more energy to reach the same speed.

4. How does temperature affect the RMS speed of molecules and atoms?

According to the ideal gas law, the RMS speed is directly proportional to the square root of the temperature. This means that as the temperature increases, the RMS speed of molecules and atoms also increases.

5. Is the RMS speed of molecules and atoms constant?

No, the RMS speed of molecules and atoms is not constant. It depends on various factors such as temperature, pressure, and the type of gas. In a gas mixture, each type of molecule or atom will have a different RMS speed based on its individual properties.

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