What is the velocity (in m/s) of an electron that has a wavelength of 3.13 x 10⁵ pm? (Mass of an electron = 9.11 x 10^-31 kg).

• A. 1543 m/s
• B. 3220 m/s
• C. 2320 m/s
• D. 3541 m/s

Answer: (C)

Verified step by step guidance

1. First, convert the wavelength from picometers (pm) to meters (m). Since 1 pm = 1 x 10^-12 m, multiply the given wavelength by this conversion factor: 3.13 x 10^5 pm * 1 x 10^-12 m/pm.
2. Use the de Broglie wavelength formula to relate the wavelength to the velocity of the electron. The formula is: λ = h / (m * v), where λ is the wavelength, h is Planck's constant (6.626 x 10^-34 Js), m is the mass of the electron, and v is the velocity.
3. Rearrange the de Broglie equation to solve for velocity (v): v = h / (m * λ).
4. Substitute the known values into the equation: Planck's constant (h = 6.626 x 10^-34 Js), mass of the electron (m = 9.11 x 10^-31 kg), and the converted wavelength in meters.
5. Calculate the velocity using the rearranged formula. Ensure all units are consistent to obtain the velocity in meters per second (m/s).