To determine the wavelength of a moving neutron, we can use the de Broglie wavelength equation, which relates the wavelength (λ) of a particle to its momentum (p) and Planck's constant (h):
λ = h / p
Where: λ = wavelength h = Planck's constant (approximately 6.626 x 10^-34 J·s) p = momentum
The momentum of a particle can be calculated as the product of its mass (m) and velocity (v):
p = m * v
Given that the speed of the neutron is 4.15 km/s, we need to convert it to meters per second:
4.15 km/s = 4.15 x 10^3 m/s
The mass of a neutron is approximately 1.675 x 10^-27 kg.
Now we can substitute the values into the equations:
p = (1.675 x 10^-27 kg) * (4.15 x 10^3 m/s)
Calculating p, we find:
p ≈ 6.948 x 10^-24 kg·m/s
Finally, we can substitute the momentum value into the de Broglie wavelength equation to find the wavelength:
λ = (6.626 x 10^-34 J·s) / (6.948 x 10^-24 kg·m/s)
Calculating λ, we find:
λ ≈ 9.519 x 10^-11 meters
Therefore, the wavelength of the neutron traveling at a speed of 4.15 km/s is approximately 9.519 x 10^-11 meters or 95.19 picometers.