A cubical box of side 1 ~m contains Boron gas at a pressure of 100 ~Nm ⁻² . During an observation time of 1 second, an atom travelling with the rms speed parallel to one of the edges of the cube, was found to make 500 hits with a particular wall, without any collision with other atoms. The total mass of gas in the box in gram is

Step-by-step solution

The side length of the cubical box is L = 1 m . The volume of the box is V = L^3 = 1 m ^3 . An atom travels with rms speed v_ rms parallel to an edge. In 1 second, it makes 500 hits on a wall. Since it travels back and forth between two opposite walls, the distance covered in one round trip is 2L = 2 m . The number of hits in 1 second is N = 500 . The time taken for one round trip is t = 2L v_ rms . The number of hits per second is 1 t = v_ rms 2L . Given v_ rms 2L = 500 , we have v_ rms = 500 2 1 = 1000 m/s . The