Estimate the number of molecules in the Earth's atmosphere. Insert your answer as \log_{10}log 10 (i.e. if you calculated 1e314, enter 314).
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The number of molecules in the Earth's atmosphere is 1.725 x 10^44 = log_{10} 1.725 + 44
- Taking the earth as a sphere of given radius 8000 km, its surface area is given as
- A = 4πr²
- A = 4π(8000 × 1000)²\ m²
- A = 8.0425 × 10^14\ m²
- We know that 1 Atm Pressure = 101,325 Pascals,
- Pressure = Force/Area ⇒ Force = Pressure × Area
- Force due to 1 Atm pressure is given by,
- F = (101,325) × ( 8.0425 x 10^14)
- ⇒ F = 8.1490 × 10^19 N
- Mass of atmosphere M = F / g
- where g is the acceleration due to gravity and g =9.81\ ms^-2
- M = (8.1490 × 10^19) / 9.81 = 8.3068 × 10^18\ kg
- We know that 1 mol of anything contains 6.0221 × 10^23 molecules.
- We get an estimate of the number of molecules in the atmosphere as
- ( 8.3068 × 10^18) x (1/ (29/10³) ) × 6.0221 × 10^23 = 1.725 × 10^44 molecules
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