Final answer:
The velocity of an electron with a mass of 9.11 x 10^-31 kg and a wavelength of 4.65 x 10^-7 m is approximately 1.563 x 10^7 m/s, calculated using the de Broglie wavelength equation.
Step-by-step explanation:
To calculate the velocity of an electron given its mass and wavelength, we can use the de Broglie equation which relates the wavelength (λ) of a particle to its momentum (p) through Planck's constant (h): λ = h / p. Since the momentum of a particle is given by its mass (m) multiplied by its velocity (v), we can rearrange for velocity as v = h / (λm).
The mass (m) of the electron is given as 9.11 x 10⁻³¹ kg, and Planck's constant (h) is approximately 6.626 x 10⁻4 J·s. Substituting these values along with the given wavelength (λ) of 4.65 x 10⁻⁷ m, we get:
v = (6.626 x 10⁻4 J·s) / (4.65 x 10⁻⁷ m × 9.11 x 10⁻³¹ kg) = (6.626 x 10⁻4) / (4.23595 x 10⁻8) m/s
Calculating this gives us the velocity v ≈ 1.563 x 10⁷ m/s.
Therefore, the electron is moving at a velocity of about 1.563 x 10⁷ meters per second.