The RMS speed of 65 g of oxygen gas is 254 m/s. Calculate the average kinetic energy of the molecules.

The molecules in a six-particle gas have velocities:

$\(\begin{aligned}\) \(\vec{v}\)_1 &= (20\(\hat{i}\) - 30\(\hat{j}\)) \(\text{ m/s}\) \\ \(\vec{v}\)_2 &= (40\(\hat{i}\) + 70\(\hat{j}\)) \(\text{ m/s}\) \\ \(\vec{v}\)_3 &= (-80\(\hat{i}\) + 20\(\hat{j}\)) \(\text{ m/s}\) \\ \(\vec{v}\)_4 &= 30\(\hat{i}\) \(\text{ m/s}\) \\ \(\vec{v}\)_5 &= (40\(\hat{i}\) - 40\(\hat{j}\)) \(\text{ m/s}\) \\ \(\vec{v}\)_6 &= (-50\(\hat{i}\) - 20\(\hat{j}\)) \(\text{ m/s}\) \(\end{aligned}\)$

Calculate (a) ${\vec{v}}_{\text{avg}}$, (b) $v_{\text{avg}}$, and (c) $v_{\text{rms}}$.

At what temperature would the average kinetic energy (Chapter 18) of a molecule of hydrogen gas (H₂) be sufficient to excite a hydrogen atom out of the ground state?

A rubidium atom (m = 85 u) is at rest with one electron in an excited energy level. When the electron jumps to the ground state, the atom emits a photon of wavelength ⋋ = 780 nm. Determine the resulting (nonrelativistic) recoil speed v of the atom.

A rubidium atom (m = 85 u) is at rest with one electron in an excited energy level. When the electron jumps to the ground state, the atom emits a photon of wavelength ⋋ = 780 nm. The recoil speed sets the lower limit on the temperature to which an ideal gas of rubidium atoms can be cooled in a laser-based atom trap. Using the kinetic theory of gases (Chapter 18), estimate this “lowest achievable” temperature.

Which of the following samples contains particles with the lowest average $kinetic energy$?

Which of the following samples will have the lowest average kinetic energy per molecule ($E=\frac{3}{2}kT$)?

Which of the following quantities measures the average kinetic energy of the particles in an ideal gas?$$

For an ideal gas, what is the average kinetic energy per molecule at temperature $T$?