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Q71E

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Found in: Page 472

### College Physics (Urone)

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 2.00×1013 K. (a) What would the average velocity vrms of hydrogen atoms be? (b) What is unreasonable about this velocity? (c) Which premise or assumption is responsible?

1. The vrms of hydrogen atoms are $7.08×{10}^{8}m/s$.
2. The result is unreasonable because it is a higher value than the speed of light.
3. This unreasonable velocity is due to the given high temperature.
See the step by step solution

## Step 1: Concept

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 2.00×1013 K. is the mass of the atom, and the mass of hydrogen is1.67×10-27 Kg.

## Step 2: Solution for part

Substitute these values into the equation.

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

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

## Step 2: Solution for part (b)

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.

## Step 3: Solution for part (c)

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.