How fast must a 56.5 g tennis ball travel in order to have a de-Broglie wavelength that is equal
to that of a photon of green light (5400 Angstroms)?
To find the speed at which a 56.5 g tennis ball must travel in order to have a de-Broglie wavelength equal to that of a photon of green light (5400 Angstroms), we can use the following equation:
λ = h / (m * v)
where:
λ is the de-Broglie wavelength,
h is Planck's constant (6.626 × 10^-34 J·s),
m is the mass of the tennis ball in kilograms, and
v is the velocity of the tennis ball in meters per second.
First, convert the mass of the tennis ball from grams to kilograms:
56.5 g = 56.5 × 10^-3 kg
Next, rearrange the equation to solve for v:
v = h / (m * λ)
Plug in the known values:
v = (6.626 × 10^-34 J·s) / (56.5 × 10^-3 kg * 5400 × 10^-10 m)
Simplify the equation:
v = 6.626 × 10^-34 J·s / (56.5 × 5400 × 10^-13 J·s·m)
Calculate the final result:
v ≈ 2.36 × 10^2 m/s
Therefore, the tennis ball must travel at approximately 2.36 × 10^2 m/s to have a de-Broglie wavelength equal to that of a photon of green light.