What is the formula to calculate the velocity of a billiard ball based on its wavelength? How can we find the velocity of a 0.400-kg billiard ball with a wavelength of 7.7 cm?

To calculate the velocity of a billiard ball based on its wavelength, we can use the formula: Wavelength = h / (m * v), where h is Planck's constant, the wavelength is the de Broglie wavelength, m is the mass of the pool ball, and v is its velocity.
Given that the billiard ball has a mass of 0.400 kg and a wavelength of 7.7 cm, we need to convert the wavelength from centimeters to meters before calculating the velocity.
First, let's convert the wavelength from cm to meters:
Wavelength = 7.7 cm = 7.7 x 10^-2 m = 0.077 m
Now, we can rearrange the formula to solve for the velocity:
v = h / (m * wavelength)
v = (6.626 x 10^-34 Js) / (0.400 kg * 0.077 m)
v = 6.626 x 10^-34 / 0.0308 ≈ 2.15 x 10^(-32) m/s
Therefore, the velocity of the 0.400 kg billiard ball, with a wavelength of 7.7 cm, is approximately 2.15 x 10^(-32) m/s.