A molecule of oxygen gas (O2) has a velocity of 2800 m/s. What is its de Broglie wavelength?
wavelength = h/mv
4.5 × 10−12 m
To find the de Broglie wavelength of a particle, you need to use the de Broglie wavelength formula:
λ = h / p,
where λ is the de Broglie wavelength, h is the Planck's constant (6.626 x 10^-34 J·s), and p is the momentum of the particle.
The momentum of a particle can be calculated using the formula:
p = m * v,
where p is the momentum, m is the mass of the particle, and v is the velocity of the particle.
In this case, we have the velocity of the oxygen gas molecule, which is 2800 m/s. However, we need to determine the momentum to calculate the de Broglie wavelength. To find the momentum, we need to know the mass of the oxygen molecule.
The molar mass of oxygen (O2) is about 32 g/mol, which can be converted to kilograms by dividing by 1000:
m = 32 g / 1000 = 0.032 kg.
Now, we can calculate the momentum:
p = m * v
= 0.032 kg * 2800 m/s.
Finally, we can calculate the de Broglie wavelength, using the momentum we just found:
λ = h / p
= (6.626 x 10^-34 J·s) / (0.032 kg * 2800 m/s).