To calculate the wavelength of a proton traveling at a given speed, we can use the de Broglie wavelength formula:
λ = h / p
Where λ is the wavelength, h is the Planck's constant (6.62607015 × 10^(-34) m^2 kg / s), and p is the momentum of the proton.
The momentum of the proton can be calculated using the equation:
p = m * v
Where m is the mass of the proton (approximately 1.6726219 × 10^(-27) kg) and v is its velocity.
Let's plug in the values and calculate the wavelength:
v = 255,000,000 m/s m = 1.6726219 × 10^(-27) kg h = 6.62607015 × 10^(-34) m^2 kg / s
p = m * v = (1.6726219 × 10^(-27) kg) * (255,000,000 m/s) ≈ 4.2710598 × 10^(-18) kg * m/s
λ = h / p = (6.62607015 × 10^(-34) m^2 kg / s) / (4.2710598 × 10^(-18) kg * m/s) ≈ 1.5509428 × 10^(-16) m
Therefore, the wavelength of a proton traveling at 255,000,000 m/s is approximately 1.5509428 × 10^(-16) meters.