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Q71E

Expert-verifiedFound in: Page 472

Book edition
1st Edition

Author(s)
Paul Peter Urone

Pages
1272 pages

ISBN
9781938168000

**Question:**** ****The temperature inside a supernova explosion is said to be 2.00×10 ^{13} K. (a) What would the average velocity v_{rms} of hydrogen atoms be? (b) What is unreasonable about this velocity? (c) Which premise or assumption is responsible?**

**Answer**

- The v
_{rms}of hydrogen atoms are $7.08\times {10}^{8}m/s$. - The result is unreasonable because it is a higher value than the speed of light.
- This unreasonable velocity is due to the given high temperature.

**The average velocity of an atom is directly related to its temperature. This is expressed as,**

${{\mathbf{v}}}_{{\mathbf{rms}}}{\mathbf{=}}\sqrt{\frac{\mathbf{3}\mathbf{kT}}{\mathbf{m}}}$

**Here, is the average velocity, is the Boltzmann constant and its value is . is the temperature in Kelvin and its value is given as 2.00×10 ^{13} K. is the mass of the atom, and the mass of hydrogen is1.67×10^{-27 }Kg. **

Substitute these values into the equation.

${v}_{rms}=\sqrt{\frac{3\times (1.38\times {10}^{-23}J/K)\times (2.00\times {10}^{13}K)}{(1.67\times {10}^{-27}Kg)}}\phantom{\rule{0ex}{0ex}}=7.04\times {10}^{8}m/s$

So, the average velocity of a hydrogen atom is $7.04\times {10}^{8}m/s$

The calculated average velocity is unreasonable because it is faster than the light. The speed of light is approximately equal to . No, objects can exceed speed. So, it is not a possible velocity.

The given premise leads to an unreasonable answer. Here, the given temperature is too high. Since the temperature is directly proportional to the velocity, it gives a higher value.

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