Question

Some incandescent light bulbs are filled with argon gas. What is the mean speed ((vₘean)) for argon atoms near the filament, assuming their temperature is 2500 K?

a) (1.44 X 10³ m/s)
b) (2.08 X 10³ m/s)
c) (2.41 X 10³ m/s)
d) (3.00 X 10³ m/s)

Answer 1

The mean speed (Vrms) of argon atoms in an incandescent light bulb at a temperature of 2500 K is calculated using the rms speed formula and is approximately 2.08 × 103 m/s. Therefore the correct answer is b) (2.08 X 10³ m/s).

Step-by-step explanation:

The student has asked for the mean speed (Vrms) of argon atoms near the filament in an incandescent light bulb at a temperature of 2500 K.

The root-mean-square (rms) speed can be calculated using the formula Vrms = sqrt(3kT/m), where k is the Boltzmann constant (1.38 × 10-23 J/K) and m is the mass of an argon atom.

Argon has an atomic mass of about 39.95 u (unified atomic mass units), which is equivalent to 39.95 × 1.66 × 10-27 kg.

Plugging in the numbers, we find the mean speed of argon atoms at this temperature to be approximately 2.08 × 103 m/s, which corresponds to option (b).