Final answer:
The rms speed of argon atoms in an incandescent light bulb at 2500 K is calculated using the rms speed formula with the given temperature and the mass of an argon atom. After computing, the rms speed is found to be close to 923 m/s.
Step-by-step explanation:
The question asks for the root-mean-square (rms) speed (vrms) of argon atoms inside an incandescent light bulb at a temperature of 2500 K. To calculate the rms speed, we can use the formula: vrms = √(3kT/m), where k is the Boltzmann constant (1.38 × 10−12 J/K), T is the temperature in kelvin, and m is the mass of an argon atom. The mass (m) of an argon atom can be found by dividing the molar mass of argon by Avogadro's number: m = 39.95 g/mol ÷ (6.022 × 1023 atoms/mol), converting grams to kilograms in the process.
To find the molar mass in kg, we convert 39.95 g to kg (39.95 g = 3.995 × 10−4 kg). Next, we insert all values into the rms speed equation:
vrms = √(3 × 1.38 × 10−12 J/K × 2500 K) / (3.995 × 10−4 kg)
Calculate the square root to find the rms speed. Plugging the numbers into a calculator yields an rms speed close to the option (b) 923 m/s, which is the correct answer to the student's question.