Final answer:
To find the wavelength of a proton moving at 1.00% of the speed of light, use the de Broglie equation and the relativistic momentum equation.
Step-by-step explanation:
To find the wavelength of a proton moving at 1.00% of the speed of light, we can use the de Broglie equation, which relates the wavelength of a particle to its momentum:
λ = h / p
Where λ is the wavelength, h is Planck's constant (6.626 x 10^-34 J·s), and p is the momentum of the proton.
Since the proton is moving at 1.00% of the speed of light, we can calculate its momentum using the relativistic momentum equation:
p = γm₀v
Where γ is the Lorentz factor (1 / √(1 - (v/c)^2)), m₀ is the rest mass of the proton (1.67 x 10^-27 kg), and v is the velocity of the proton.
After calculating the momentum, we can substitute it into the de Broglie equation to find the wavelength.
Using the given values, the correct answer is option d) 13.21 pm.