Chapter 13, Problem 47P

To determine

To Calculate:The root means square speed of helium atoms.

Answer to Problem 47P

The root mean square speed of the helium gas is $6\times {10}^3\raisebox{1ex}{$\text{m}$}\!\left/ \!\raisebox{-1ex}{$\text{s}$}\right.$ .

Explanation of Solution

Given info:

Temperature, $\text{T}\text{=}\text{6000K}$ .

Mass number of helium, $z=4$ .

Boltzmann constant, $k\text{=}\text{1}{\text{.38×10}}^{\text{-23}}\text{J/K}$ .

Formula used:

The root mean square speed of the helium gas is:

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

Here, $k$ is the Boltzmann constant,

  $T$ is the temperature of helium,

  $m$ is mass of the helium.

Calculation:

Substituting the given values in the formula then the result is,

  $\begin{array}{c}{\text{v}}_{\text{rms}}\text{=}\sqrt{\frac{\text{3kT}}{\text{m}}}\\ \text{=}\sqrt{\frac{\text{3×}\left(\text{1}{\text{.38×10}}^{\text{-23}}\text{J/K}\right)\text{×}\left(\text{6000K}\right)}{\text{4}\text{.0×1}{\text{.66×10}}^{\text{-27}}\text{kg}}}\\ \text{=}{\text{6×10}}^{\text{3}}\text{m/s}\end{array}$

Conclusion:

The root means square speed is $6\times {10}^3\raisebox{1ex}{$\text{m}$}\!\left/ \!\raisebox{-1ex}{$\text{s}$}\right.$ .