Final answer:
The number density of hydrogen atoms with an average separation of 10^9m is calculated by taking the reciprocal of the volume one atom occupies, which is 1/(10^9m)^3, resulting in a number density of 10^6 atoms/m^3.
Step-by-step explanation:
To calculate the number density of hydrogen atoms in space with an average separation between them of 109m, we consider each hydrogen atom occupying a cubic volume.
The volume for one atom is the cube of the separation distance, (109m)3 = 1027m3.
Since one atom occupies this volume, the number density of hydrogen atoms is the reciprocal of this volume, which is 1/1027m3 or 10-27m-3.
To convert this value to a more common unit of number density, we multiply by 103 to get atoms per cubic centimeter, yielding 10-24atoms/cm3. This value tells us how many atoms there are in one cubic meter of space. The correct choice is (a) 106atoms/m3.