Question

Question: Calculate the RMS speed of helium atoms at 1000k. Molar mass of helium atoms is$\mathbf{4}\mathbf{.}\mathbf{0026}\frac{\mathbf{g}}{\mathbf{mol}}$.

Short answer

Answer

The RMS speed of helium atoms at 1000 k is$2.50\times {10}^3\frac{\text{m}}{\text{s}}$.

Step-by-step solution

Given

The temperature is T = 1000 k

Determining the concept

Find the RMS speed from its formula in terms of R, temperature, and molar mass.

Formula is as follow:

$v=\sqrt{\frac{3RT}{M}}$

Here, M is mass, Tis temperature, v is velocity and R is universal gas constant.

Determining the RMS speed of helium atoms at 1000 K

The RMS speed of helium atoms is,

$v=\sqrt{\frac{3RT}{M}}$

Molar mass of helium is,

$M=4\times {10}^{-3}\frac{\text{kg}}{\text{mol}}$

Substitute the values in the equation for velocity and solve as:

$$\begin{gathered} v=\sqrt{\frac{3\left(8.314\right)\left(1000\right)}{4\times {10}^{-3}}} \\ v=2497 \\ \approx 2.50\times {10}^3\frac{\text{m}}{\text{s}} \end{gathered}$$

Hence, the RMS speed of helium atoms at 1000 K is $2.50\times {10}^3\frac{\text{m}}{\text{s}}$.