Final answer:
The de Broglie wavelengths of both an electron and a bowling ball with the same kinetic energy can be calculated using their mass and velocity, with the photon wavelength calculation relying on the photon's energy-wavelength relationship.
Step-by-step explanation:
The de Broglie wavelength (λ), which is associated with any moving object, is given by the equation λ = h / p, where h is Planck's constant (6.626 x 10-34 m2 kg / s) and p is the momentum of the object (mass x velocity). In our case, to find the momentum from kinetic energy (KE), we use KE = p2 / (2m), and thus p = √(2mKE). As electrons and bowling balls have significantly different masses, their associated wavelengths will be vastly different.
(a) The de Broglie wavelength of the electron can be calculated by first converting the kinetic energy (KE) from electronvolts (eV) to joules (J), using the conversion factor 1 eV = 1.602 x 10-19 J.
(b) The de Broglie wavelength of the bowling ball can similarly be calculated by converting its KE to joules and solving for p and subsequently λ.
(c) The wavelength of a photon with energy 4.25 eV is found using the energy-wavelength relationship for photons, E = hc / λ, where c is the speed of light (approximately 3.00 x 108 m/s).