To calculate the wavelength of a neutron, you can use the de Broglie wavelength formula:
wavelength = h / (mass * velocity)
Where:
- wavelength is the de Broglie wavelength of the neutron,
- h is the Planck's constant (approximately 6.62607015 × 10^-34 m² kg/s),
- mass is the mass of the neutron, and
- velocity is the speed of the neutron.
However, we need to convert the mass of the neutron from grams to kilograms for consistent units. The mass of the neutron is approximately 1.67493 × 10^-24 grams, which is equal to 1.67493 × 10^-27 kilograms.
Now we can calculate the wavelength:
wavelength = (6.62607015 × 10^-34 m² kg/s) / (1.67493 × 10^-27 kg * 85.0 m/s)
Calculating the expression:
wavelength ≈ 2.445 × 10^-10 meters
To convert the wavelength to nanometers (nm), we multiply by 10^9:
wavelength ≈ 2.445 × 10^-1 nm
Therefore, the wavelength of a neutron traveling at a speed of 85.0 m/s is approximately 0.245 nm.