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Answer :
At standard temperature and pressure, the particle flux of hydrogen molecules is approximately 4.57139 x 10²â¸ particles per square meter per second.
The particle flux, also known as the number flux or particle current density, represents the number of particles passing through a unit area per unit time. It's given by the formula:
Particle Flux (J) = Number Density (η) × Mean Speed (v)
Where:
Number Density (η) is the number of particles per unit volume.
Mean Speed (v) is the average speed of the particles.
In this case, you're dealing with hydrogen molecules. The number density of a gas is given by the ideal gas law:
n = Pressure (P) / (k * Temperature (T))
Where:
Pressure (P) is the pressure of the gas.
k is Boltzmann's constant (1.380649 × 10⻲³ m² kg s⻲K⻹).
Temperature (T) is the temperature of the gas in Kelvin.
J = n * v
J = (2.6867 x 10²âµ) * (1.70 x 10³)
Calculate J:
J ≈ 4.57139 x 10²â¸particles/(m² s)
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The particle flux of hydrogen molecules at standard temperature and pressure is approximately 4.573 x 10²â¸ molecules/(m²*s).
The particle flux (also known as particle flow rate or particle current density) is a measure of the number of particles passing through a unit area per unit time. It can be calculated using the formula:
Particle Flux (J) = Number Density (n) * Mean Speed (v)
Where:
- Number Density (n) is the number of particles per unit volume.
- Mean Speed (v) is the average speed of the particles.
In this case, you're given the mean speed of hydrogen molecules
(v = 1.70 × 10³ m/s) at standard temperature and pressure (STP).
For an ideal gas at STP, the number density is approximately 2.69 x 10²âµ molecules per cubic meter.
Plug the values into the formula:
J = n * v
J = (2.69 x 10²âµ molecules/m³) * (1.70 × 10³ m/s)
J = 4.573 x 10²â¸ molecules/(m²*s)
So, the particle flux of hydrogen molecules at standard temperature and pressure is approximately 4.573 x 10^28 molecules/(m²*s).
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