How Does Temperature Affect the RMS Speed of Helium Atoms?

[BuBbLeS01]

Homework Statement

What is the RMS speed of Helium atoms when the temperature of the Helium gas is 247 K? (Possibly useful constants: the atomic mass of Helium is 4.00 AMU, the Atomic Mass Unit is: 1 AMU = 1.66×10-27 kg, Boltzmann's constant is: kB = 1.38×10-23 J/K.)

What would be the RMS speed, if the temperature of the Helium gas was doubled?

Homework Equations

sq rt of 3RT/M

The Attempt at a Solution

is that the right equation to use? I am having a hard time with this one

 

[hage567]

Yes, you can use that equation.

 

[ogb p]

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I would like to clarify that the equation you have suggested is not entirely correct. The correct equation for calculating the RMS speed of Helium atoms is v = √(3RT/M), where v is the RMS speed, R is the gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and M is the molar mass of Helium.

Using this equation, the RMS speed of Helium atoms at a temperature of 247 K would be approximately 1206 m/s.

If the temperature of the Helium gas was doubled to 494 K, the RMS speed would also double to approximately 2412 m/s. This is because the RMS speed is directly proportional to the square root of temperature.

I hope this helps clarify the correct equation and how the RMS speed changes with temperature.