Answer:
The time required is 20 μs
Explanation:
Here is the data provided:
temperature = 20°C = 293 K
radius = 1 cm
atomic mass of air = 29 u
To determine
the duration for air to refill the vacuum space
solution:
We calculate the root mean square velocity of air particles. This can be expressed as:

where m indicates mass, t is temperature, v is speed, and R is the ideal gas constant, which is approximately 8.3145 (kg·m²/s²)/K·mol.
v =
............................1
v =
Resulting in v = 501.99 m/s.
<pNow, to cover the distance of 1 cm,<pThe duration needed for air is calculated as:
time taken = 
which gives us:
time taken = 
so, time taken = 19.92 ×
seconds = 20μs.
Thus, the required time is 20 μs.