How much faster does a helium atom travel than a nitrogen molecule at thesame temperature?
At the same temperature, the average speed of gas particles is directly proportional to the square root of their mass.
The molecular mass of helium is approximately 4 atomic mass units (u), and the molecular mass of nitrogen is approximately 28 u.
Let Vh and Vn be the average speeds of helium and nitrogen, respectively.
According to the kinetic theory of gases, the ratio of their average speeds can be found using the formula:
Vh/Vn = √(Mn/Mh)
Vh/Vn = √(28/4) = √7 ≈ 2.65
Therefore, a helium atom travels approximately 2.65 times faster than a nitrogen molecule at the same temperature.
To compare the speed of a helium atom and a nitrogen molecule at the same temperature, we can use the root mean square velocity formula given by:
v = √ ((3kT) / m)
Where:
v = root mean square velocity
k = Boltzmann constant (1.38 x 10^-23 J/K)
T = temperature (in Kelvin)
m = mass (in kg)
For helium:
m(He) = 4.0 atomic mass units (amu)
m(He) = 4.0 x 1.66 x 10^-27 kg (1 amu = 1.66 x 10^-27 kg)
For nitrogen:
m(N2) = 28.0 amu
m(N2) = 28.0 x 1.66 x 10^-27 kg
Let's assume the temperature is 300 Kelvin.
For helium:
v(He) = √((3 x 1.38 x 10^-23 J/K x 300 K) / (4.0 x 1.66 x 10^-27 kg))
For nitrogen:
v(N2) = √((3 x 1.38 x 10^-23 J/K x 300 K) / (28.0 x 1.66 x 10^-27 kg))
Calculating these velocities, we find:
v(He) ≈ 1671 m/s
v(N2) ≈ 515 m/s
Therefore, the helium atom travels approximately 1671 m/s, while the nitrogen molecule travels about 515 m/s at the same temperature. Therefore, the helium atom is faster than the nitrogen molecule.