How fast must a 144 g baseball travel in order to have a de Broglie wavelength that is equal to that of an x-ray photon with = 100. pm?
To calculate the velocity of the baseball, we can use the de Broglie wavelength formula:
λ = h / mv
where λ is the wavelength, h is the Planck constant (6.62607015 × 10^-34 J·s), m is the mass of the baseball, and v is the velocity.
Given that the mass of the baseball is 144 g (0.144 kg) and that the wavelength of the x-ray photon is 100 pm (100 × 10^-12 m), we can rearrange the formula to solve for v:
v = h / (mλ)
Now, let's plug in the values:
v = (6.62607015 × 10^-34 J·s) / ((0.144 kg) × (100 × 10^-12 m))
Simplifying the expression:
v = (6.62607015 × 10^-34) / (0.0144 × 10^-12)
v = 4.59335443 × 10^22 m/s
Therefore, the baseball must travel at a velocity of approximately 4.59 × 10^22 m/s to have a de Broglie wavelength equal to that of an x-ray photon with a wavelength of 100 pm.