Final answer:
To calculate the velocity of an electron to have a de Broglie wavelength of 1.00 angstrom, the de Broglie wavelength formula is used, and the result is approximately 7.28 × 10^6 meters per second.
Step-by-step explanation:
The question asks to find the velocity at which an electron must travel to have a de Broglie wavelength of 1.00 angstroms (1.00 × 10-10 meters). To solve this, we'll use the de Broglie wavelength formula: λ = h / p, where λ is the wavelength, h is Planck's constant (6.626 × 10-34 m2 kg / s), and p is the momentum of the particle (product of mass and velocity, m × v).
To find the velocity (v), we can rearrange the formula to get v = h / (m × λ). The mass of an electron (m) is known to be 9.11 × 10-31 kg. Substituting these values, the calculation for velocity (v) is as follows:
v = 6.626 × 10-34 m2 kg / s / (9.11 × 10-31 kg × 1.00 × 10-10 m)
= 6.626 × 10-34 / (9.11 × 10-31 × 1.00 × 10-10)
= 7.28 × 106 m/s
Therefore, an electron must travel at approximately 7.28 × 106 meters per second to have a de Broglie wavelength of 1.00 angstrom.