What is the mean speed of hydrogen atoms at 50K?

[Grand]

Homework Statement

Dear all, I have to calculate the mean speed of hydrogen atoms, at temperature of 50K.

Homework Equations

Of course:
$$<v>=\sqrt{\frac{8k_BT}{\pi m}}$$

The Attempt at a Solution

However, when I attempt to calculate it,
$$m=\frac{2}{6.022x10^{23}}$$
$$k_B=1.3807x10^{-23}$$

I get a value of 23 ms-1 which is obviously not correct, so could anyone poit me where am I going wrong?

 

[graphene]

You are making a mistake while calculating m. Be careful about the units.
& you are talking about H atom, not $$H_2$$ molecule.

 

[vela]

I get a value of 23 ms-1 which is obviously not correct, so could anyone poit me where am I going wrong?

Is it obvious? (I'm not saying your answer is correct, but that it's just not obvious it's obviously wrong.) The temperature is pretty low, so you should expect a relatively low speed.

 

[Grand]

Thank you, but then what is the correct calculation of the mass? When you're told that the mass of something is x atomic units, is this the mass per mole or the mass expressed in multiples of the mass of the proton?

 

[ehild]

The unit of mass has to match to the unit of the Boltzmann constant so as to get the speed in m/s. k_B=1.3807x10^-23 J/K. You know that J=kg*m²/s². You need the mass of one hydrogen atom in kg units.

ehild

 

[Grand]

OK, I understand that, but what is the numerical constant that I should multiply the atomic weight by so as to get this result?

 

[vela]

Graphene basically told you what your mistake is. What's the molar mass of a hydrogen atom as opposed to a hydrogen molecule?

 

[Borek]

Also: when you say molar mass of something is 2, it is 2 of what? Tonnes? Pounds? Stones?

 

[graphene]

hey grand

Atomic masses are conveniently expressed in http://en.wikipedia.org/wiki/Atomic_mass_unit" . The other constants in your expression are in SI units. So u'll have to convert m from amu to kg.

 

[ehild]

OK, I understand that, but what is the numerical constant that I should multiply the atomic weight by so as to get this result?

The "atomic weight" is really the mass of one mole of the atomic material and is given in grams. The atomic weight or atomic mass of the atomic hydrogen is 1 g. You have to multiply it by 0.001 to convert to kg units, and divide by the Avogadro number to get the mass of one atom.



ehild