What is the de Broglie wavelength of an oxygen molecules having tha end speed,characteristics of the Maxwell distribution at 27 degree Celsius.
Pls give the answer
To determine the de Broglie wavelength of an oxygen molecule, we need to use the formula:
λ = h / p
where λ is the de Broglie wavelength, h is Planck's constant, and p is the momentum of the particle.
First, we need to find the momentum of the oxygen molecule. The momentum is given by the mass (m) of the particle multiplied by its velocity (v):
p = m * v
To calculate the momentum, we need to know the mass of an oxygen molecule. The molecular mass of oxygen (O₂) is approximately 32 g/mol.
Next, we need to find the velocity of the oxygen molecule. The Maxwell-Boltzmann distribution describes the distribution of speeds for particles in a gas at a given temperature. The distribution states that the most probable speed (vmp) is given by the following formula:
vmp = √(2 * k * T / m)
where k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the molecule.
To convert the temperature from Celsius to Kelvin, we add 273:
T = 27 + 273 = 300 K
Now, we can calculate the most probable speed:
vmp = √(2 * k * 300 / 32)
To compute the de Broglie wavelength, we substitute the values of h, p, and v into the formula:
λ = h / p
Lastly, we evaluate the expression to find the de Broglie wavelength of an oxygen molecule with the given characteristics.