Velocity of a Billiard Ball Calculation
What is the velocity of a 0.400-kg billiard ball if its wavelength is 5.1 cm (large enough for it to interfere with other billiard balls)?
How can we calculate the velocity of the billiard ball based on its mass and wavelength?
Answer:
The velocity of the billiard ball can be calculated using the de Broglie wavelength formula:
λ = h / p
Where:
λ is the wavelength
h is the Planck constant (6.626 x 10^-34 J s)
p is the momentum of the particle
The momentum can be calculated as:
p = mv
Where:
m is the mass of the particle
v is its velocity
Rearranging the first equation gives:
v = p / m = h / (mλ)
Substituting the given values:
v = (6.626 x 10^-34 J s) / (0.400 kg x 5.1 x 10^-2 m) = 3.26 m/s
Velocity of a Billiard Ball Calculation
Calculating the velocity of a billiard ball with a mass of 0.400 kg and a wavelength of 5.1 cm involves using the de Broglie wavelength formula. The formula relates the wavelength of a particle to its momentum and the Planck constant.
By rearranging the formula and substituting the given values, we can find that the velocity of the billiard ball is 3.26 m/s. This calculation allows us to determine how fast the billiard ball is moving based on its mass and wavelength.
Understanding the relationship between mass, velocity, and wavelength in this context provides valuable insights into the behavior of particles at the quantum level. By applying fundamental physics principles, we can solve complex problems and uncover the underlying mechanisms of particle motion.