Final answer:
The kinetic energy of a proton can be found using its de Broglie wavelength by applying the formula K = (h / 2λ)^2 / (2m), with Planck's constant and the proton's mass.
Step-by-step explanation:
The question asks us to find the kinetic energy of a proton given its de Broglie wavelength. To find the kinetic energy of the proton, we can use the de Broglie wavelength formula: λ = h / p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the proton.
The momentum p can be expressed in terms of the proton's mass (m) and velocity (v) as p = mv, but it can also be related to kinetic energy (K) by the equation p = √(2mK), assuming the proton is nonrelativistic. Therefore, we can solve for kinetic energy using the formula K = (h / (2λ))^2 / (2m). Here, h is Planck's constant (6.62607015 × 10−15 J·s), λ is the given wavelength (1.000 u00d7 10−15 m), and m is the mass of the proton (1.6726219 × 10−27 kg).
The calculation would result in the kinetic energy of the proton, which could be expressed in joules or electronvolts, as preferred.