How fast should a 58.1g tennis ball travel to have a de Broglie wavelength that is equal to that of a photon of green light (5.40 X 10^3 angstroms)?
Wavelength = h/mv
Convert 5.40E3 A to meters (5.40E3 Angstroms = 5.40E3 x 10^-8 cm)and substitute for wavelength. m is in kg and v in m/s
To calculate the speed of the tennis ball, we can use the de Broglie wavelength formula:
λ = h / p
where λ is the wavelength, h is the Planck's constant (6.626 x 10^-34 Js), and p is the momentum of the tennis ball.
First, let's convert the given de Broglie wavelength to meters:
5.40 x 10^3 Å = 5.40 x 10^3 x 10^-10 m = 5.40 x 10^-7 m
The momentum (p) of an object can be calculated using the formula:
p = m * v
where m is the mass and v is the velocity.
Given:
Mass of the tennis ball (m) = 58.1 g = 58.1 x 10^-3 kg
We rearrange the formula to solve for velocity:
v = p / m
Substituting the given values, we get:
v = (h / λ) / m
v = (6.626 x 10^-34 Js) / (5.40 x 10^-7 m) / (58.1 x 10^-3 kg)
v ≈ 2.34 m/s
Therefore, the tennis ball should travel at approximately 2.34 m/s to have a de Broglie wavelength equal to that of a photon of green light.
To find the speed of a tennis ball that would result in a de Broglie wavelength equal to that of a photon of green light, you can 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 Js),
p is the momentum of the object.
To find the momentum, you need to find the velocity of the tennis ball. Let's assume the tennis ball has a mass of 58.1 grams (0.0581 kg).
First, convert the given wavelength from angstroms to meters:
5.40 x 10^3 angstroms = 5.40 x 10^-7 meters
Now, rearrange the formula to solve for momentum:
p = h / λ
Plug in the values:
p = (6.626 x 10^-34 Js) / (5.40 x 10^-7 meters)
Calculate the value of momentum.
Next, use the momentum to find the velocity. The momentum (p) of an object is given by the equation:
p = m * v
Where:
m is the mass of the object,
v is the velocity.
Rearrange the equation to solve for velocity:
v = p / m
Plug in the values:
v = (momentum) / (0.0581 kg)
Calculate the velocity.
This calculated velocity is the speed at which the tennis ball should travel in order to have a de Broglie wavelength equal to that of a photon of green light.