Final answer:
The root mean square (RMS) average speed of atoms in a sample of neon gas can be calculated using the formula u_rms = sqrt((3kT)/m). To find the mass of a neon atom, we need to know the molar mass of neon gas and Avogadro's number. Substituting the given values, we find the RMS speed to be 505 m/s.
Step-by-step explanation:
The root mean square (RMS) average speed of atoms in a sample of neon gas can be calculated using the formula:
urms = √((3kT)/m)
Where:
- urms is the RMS speed
- k is the Boltzmann constant (1.38 x 10-23 J/K)
- T is the temperature in Kelvin
- m is the mass of an atom
To find the mass of a neon atom, we need to know the molar mass of neon gas (20.18 g/mol) and Avogadro's number (6.022 x 1023 molecules/mol). Converting the molar mass to kilograms, we get:
m = (20.18 g/mol) / (6.022 x 1023 molecules/mol) x (1 mol / 1000 g) x (1 kg / 1000 g) = 3.35 x 10-26 kg
Substituting the given values into the formula:
urms = √((3 x 1.38 x 10-23 J/K x 273 K) / (3.35 x 10-26 kg))
Solving for urms, we get:
urms = 505 m/s