Final answer:
To find the speed of a proton with a given de Broglie wavelength, the de Broglie equation should be used in conjunction with the known mass of the proton. Inserting the values into the rearranged de Broglie equation yields a speed of approximately 3.73 x 10^7 m/s for the proton.
Step-by-step explanation:
The question pertains to the concept of the de Broglie wavelength and its relation to the velocity of a particle in quantum mechanics within the field of physics. Using the de Broglie wavelength formula 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, we can solve for the speed (v) of the proton.
First, we express the momentum (p) of the proton as the product of its mass (m) and velocity (v). We know the mass of a proton is approximately 1.67 x 10-27 kg. Thus, p = mv = (1.67 x 10-27 kg) · v.
Next, we can rearrange the de Broglie equation to solve for v: λ = h/(mv), so v = h/(mλ). Substituting in the given values, v = (6.626 x 10-34 J·s) / ((1.67 x 10-27 kg) · (101 x 10-12 m)). Calculating this gives us v ≈ 3.73 x 107 m/s, which matches answer choice (b).