You are constructing an improvised detector for radon gas, using the cooling core from an old refrigerator capable of cooling air to \(255 \mathrm{~K}\), a detector tube \(50 \mathrm{~mm}\) long, a vacuum pump to evacuate the tube, and an electric circuit that can measure the time interval needed for gas particles to travel a given distance. To determine if there is radon in the air in your room, you intend to inject samples of the air into the evacuated tube and measure the time interval needed for particles in the sample to travel from one end of the tube to the other and their root-mean-square speed for the trip.

(a) To what scale of measurement should you set the time-interval sensor if you want to detect the monatomic radon atoms? (Ignore any collisions between these atoms and other particles in the sample.)

(b) Can you suggest any modifications to this device to improve accuracy?

(c) Do you think you will need to calibrate your system if you have to make the more realistic assumption that the collisions between radon atoms and other particles in the sample cannot be ignored? If so, why?