A molecule of oxygen gas (O2 ) has a velocity of 2800 m / s. What is its de Broglie wavelength?
wavelength = h/mv
4.5 X 10^-12m
1.2x10^-14
To find the de Broglie wavelength of a particle, you can use the de Broglie wavelength equation:
λ = h / p
Where:
- λ is the de Broglie wavelength
- h is the Planck's constant (approximately 6.626 × 10^-34 m^2 kg / s)
- p is the momentum of the particle
In this case, you need to find the momentum of the oxygen gas molecule. The momentum (p) is given by the equation:
p = m * v
Where:
- p is the momentum
- m is the mass of the particle
- v is the velocity of the particle
The molecular mass of oxygen (O2) is approximately 32 g/mol, which is equivalent to 0.032 kg/mol. Since you have a single molecule, you need to convert it to kilograms:
mass = 0.032 kg/mol / 6.022 × 10^23 molecules per mol
Now you can calculate the momentum:
p = mass * velocity
Substituting the values:
p = (0.032 kg/mol / 6.022 × 10^23 molecules per mol) * 2800 m/s
Next, you can calculate the de Broglie wavelength by dividing Planck's constant by the momentum:
λ = h / p
Substituting the values:
λ = (6.626 × 10^-34 m^2 kg / s) / [(0.032 kg/mol / 6.022 × 10^23 molecules per mol) * 2800 m/s]
Simplifying the equation will give you the de Broglie wavelength of the oxygen gas molecule.