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### Speed of Atoms

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Date: 02/25/2002 at 03:57:03
From: Yasser
Subject: Can the speed of light be broken by this?..

Speed of light = 300 000km/sec.

What is the speed of the atoms or molecular activity of something as
hot as the sun? Will this not be faster than the speed of light?
```

```
Date: 02/25/2002 at 09:45:52
From: Doctor Rick
Subject: Re: Can the speed of light be broken by this?..

Hi, Yasser.

No, it won't. The average kinetic energy of the molecules of a
substance is 3/2 times the Boltzmann constant, k = 1.38*10^-23 J/K,
times the temperature. The core of the sun is about 1.5*10^7 K,
according to this site from the Princeton Plasma Physics Laboratory:

Fusion - Physics of a Fundamental Energy Source
From Core to Corona - Layers of the Sun
http://fusedweb.pppl.gov/CPEP/Chart_Pages/5.Plasmas/SunLayers.html

Therefore the average kinetic energy is

E = (3/2)(1.38*10^-23 J/K)(1.5*10^7 K)
= 3.1 * 10^-16 J

If we assume non-relativistic conditions, the kinetic energy of a
molecule of mass m and velocity v is E = (1/2)mv^2. Solving for v and
assuming the molecules are hydrogen (with mass 1.67*10^-27 kg), we get

v = sqrt(2E/m)
= sqrt(2*3.1*10^-16 J/1.67*10^-27 kg)
= sqrt(3.713*10^11 m^2/s^2)
= 6.09*10^5 m/s

This is ony 1/500 of the speed of light, 3.0*10^8 m/s. It is nowhere
near relativistic. But even if I obtained a speed greater than the
speed of light, it would not mean that the molecules were moving
faster than the speed of light; it would only mean that my assumption
of non-relativistic conditions was incorrect. (I only made this
assumption in order to find out quickly whether we were in the
relativistic domain.) We would have to use the relativistic formula
for kinetic energy instead:

E = mc^2/sqrt(1 - v^2/c^2) - mc^2

If you solve this for v, you'll find that, no matter how high the
kinetic energy E is, the velocity v will still be below the speed of
light, c.

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Physics/Chemistry

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