Find the deBroglie wavelength of a 0.10kg ball moving at 19.0m/s? Why don’t we see this wave?
ok so we start out with this equation...
λ = h/p
so...
λ = (6.63E-34 J-s)/(0.1 kg x 19 m/s)
λ = 3.489E-34 m
and we don't see this wave because..well...look at its size o.O
To find the de Broglie wavelength of the ball, we 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 J·s), and p is the momentum of the ball.
To find the momentum (p) of the ball, we can use the equation:
p = m * v
where p is the momentum, m is the mass of the ball, and v is the velocity of the ball.
Substituting the values into the equation, we have:
p = 0.10 kg * 19.0 m/s
p = 1.9 kg·m/s
Now, we can use the momentum to calculate the de Broglie wavelength:
λ = h / p
λ = (6.626 x 10^-34 J·s) / (1.9 kg·m/s)
Using a calculator, we obtain:
λ ≈ 3.48 x 10^-34 m
Now, to address your second question - "Why don’t we see this wave?" The de Broglie wavelength describes the wavelength of a particle-wave duality, but for macroscopic objects like a ball, the corresponding wavelength is extremely small. In the case of the 0.10 kg ball moving at 19.0 m/s, the de Broglie wavelength is on the order of 10^-34 m. This wavelength is exceptionally smaller than the scale of everyday objects and cannot be detected or observed with the naked eye.
Therefore, while the ball technically has a de Broglie wavelength, it is undetectable in our everyday experience. The macroscopic nature of the ball makes its wave-like properties negligible, and we perceive it purely as a classical, massive object.