# Thermal energy from random velocity calculation

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I have a hydrogen atom with a random velocity of;

18.0 x 10^3 m/s

it's thermal energy therefore is;

h=planck's constant

v=frequency of light

E = h x v / 18.0 x 10^3

E = (4.135 x 10^-15)(3 x 10^8 m/s) / 18.0 x 10^3

E= 6.89^-11 Jules/sec

Hoping I've got this right, I've been scratching my head over it for a little while.

Edited by johnrt
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I'm not sure what you are trying to do. "v' is the Greek letter nu (often used to denote frequency), not the Latin letter v (often used to denote velocity). You haven't given a frequency. Also, thermal energy only makes sense for a collection of atoms, not for a single atom. It does make sense to talk about the average thermal energy of members of a collection.

Can you give a little more information about what you're trying to do? Are you trying to find the kinetic energy of the atom?

Edited by George Jones
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I'm not sure what you are trying to do. "v' is the Greek letter nu (often used to denote frequency), not the Latin letter v (often used to denote velocity). You haven't given a frequency. Also, thermal energy only makes sense for a collection of atoms, not for a single atom. It does make sense to talk about the average thermal energy of members of a collection.

Can you give a little more information about what you're trying to do? Are you trying to find the kinetic energy of the atom?

George,

The question I am trying to answer gives the information that hydrogen atoms in the photosphere of a star have random velocities of 18.0 x10^3 m/s. No other values are given.

The question is - calculate the typical thermal energy of a hydrogen atom and estimate the temperature of the photosphere.

Edited by johnrt
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I guess that you want the kinetic energy, and t hen the equipartition theorem can be used to approximate the temperature, but you might not have heard of the equipartition theorem.

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I guess that you want the kinetic energy, and t hen the equipartition theorem can be used to approximate the temperature, but you might not have heard of the equipartition theorem.

Nope I haven't, it's not covered in any of the course notes that I have, so I doubt that can be the way by which the question is intended to be answered.

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Do your notes say anywhere that the average thermal energy per atom is 3*k*T/2, where k is Boltzmann's constant and T is temperature?

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The question's looking for you to apply 1/2mv^2 = 3/2 kT

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Hmmm.

My notes only mention the Steffan Boltzmann law in relation to calculating luminosity;

L = 4πR^2 σ T^4

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Hmmm.

My notes only mention the Steffan Boltzmann law in relation to calculating luminosity;

L = 4πR^2 σ T^4

This is the power (energy per unit time) radiated by a spherical (ideal) blackbody, and I'm afraid it doesn't help for this problem.

There is nothing about k*T in the thermal energy section of your notes (or text)?

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Ahh, Ok.

I have found the section of notes that relates to the Boltzmann constant and thermal energy.

However this is in a much later section of notes that my questions aren't meant to cover. So now I really am confused.

I think an email to my tutor is called for.

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Ahh, Ok.

I have found the section of notes that relates to the Boltzmann constant and thermal energy.

However this is in a much later section of notes that my questions aren't meant to cover. So now I really am confused.

I think an email to my tutor is called for.

Yes, I think so. Good luck!

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• 3 months later...

Have you found the answer to this question? It's relatively simple. I can help if you want..

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Have you found the answer to this question? It's relatively simple. I can help if you want..

Indeed I have!

E = 1/2 mv^2

E = 0.5 x 1.6735x10^-27 (mass of hydrogen atom) x 18x10^3 (velocity)

E = 2.7x10^-19 Jules

Thanks for the offer though!

Edited by johnrt

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