What is the de Broglie wavelength of an oxygen molecule, O2, traveling at 503 m/s?
wavelength = h/mv
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To find the de Broglie wavelength of an object, we can use the de Broglie wavelength equation:
λ = h / p
where λ represents the wavelength, h is the Planck's constant (h = 6.626 x 10^-34 J s), and p is the momentum of the object.
To calculate the momentum, we can use the formula:
p = m * v
where p is the momentum, m is the mass of the object, and v is its velocity.
The first step is to find the mass of an oxygen molecule, O2. The molar mass of O2 is approximately 32 g/mol. To convert grams to kilograms, we divide by 1000:
mass (m) = 32 g / 1000 = 0.032 kg
Next, we substitute the values into the momentum equation:
p = (0.032 kg) * (503 m/s)
Calculating the product gives us:
p ≈ 16.096 kg·m/s
Now, we apply this momentum value to the de Broglie wavelength equation:
λ = (6.626 x 10^-34 J s) / (16.096 kg·m/s)
Evaluating the expression gives us the de Broglie wavelength:
λ ≈ 4.11 x 10^-36 meters
Thus, the de Broglie wavelength of an oxygen molecule traveling at 503 m/s is approximately 4.11 x 10^-36 meters.