Final answer:
Using the de Broglie wavelength formula and converting the necessary units for mass and velocity, the wavelength of an electron traveling with a velocity of 7.0 × 103 km/s is calculated to be 1.03 × 10-10 meters. This answer is not one of the provided options.
Step-by-step explanation:
To calculate the wavelength of an electron traveling with a velocity of 7.0 × 103 km/s, we will use the de Broglie wavelength formula, which relates the wavelength of a particle to its momentum. The formula is given by λ = h/(mv), where λ is the wavelength, h is Planck's constant, m is the mass of the electron, and v is the velocity of the electron.
The mass of the electron should be converted from grams to kilograms (1 g = 1 × 10-3 kg), so m = 9.1 × 10-28 g = 9.1 × 10-31 kg. The velocity should also be converted from km/s to m/s, so we have v = 7.0 × 103 km/s = 7.0 × 106 m/s.
Using h = 6.626 × 10-34 Js (Planck's constant), we can substitute the values into the de Broglie equation to calculate the wavelength:
λ = λ = 6.626 × 10-34 Js / (9.1 × 10-31 kg × 7.0 × 106 m/s) = 1.03 × 10-10 meters.
Therefore, none of the given options (a) 6.63 × 10-10 m, (b) 8.21 × 10-10 m, (c) 5.43 × 10-10 m, or (d) 9.82 × 10-10 m is correct. The actual answer is 1.03 × 10-10 m, which is not listed among the options.