Calculate the de Broglie wavelength of an electron traveling with a speed of 3.21 × 10^5 m/s. Assume the mass of an electron is 9.11 × 10^-31 kg.

• A. 3.67 × 10^-12 m
• B. 2.27 × 10^-9 m
• C. 5.12 × 10^-8 m
• D. 1.45 × 10^-10 m

Answer: (B)

Verified step by step guidance

1. First, understand the concept of de Broglie wavelength, which is given by the formula: λ = h / (mv), where λ is the wavelength, h is Planck's constant (6.626 × 10^-34 Js), m is the mass of the particle, and v is the velocity of the particle.
2. Identify the given values: the speed of the electron is 3.21 × 10^5 m/s, and the mass of the electron is 9.11 × 10^-31 kg.
3. Substitute the known values into the de Broglie wavelength formula: λ = (6.626 × 10^-34 Js) / ((9.11 × 10^-31 kg) * (3.21 × 10^5 m/s)).
4. Perform the multiplication in the denominator: multiply the mass of the electron by its velocity.
5. Divide Planck's constant by the result from the previous step to find the de Broglie wavelength of the electron.