28.7k views
1 vote
If the wavelength of an electron is 5.00 x 10²⁷ m, how fast is it moving?

User Famzah
by
8.4k points

1 Answer

0 votes

Final answer:

To find the velocity of an electron with a specific wavelength, we use the de Broglie equation. The calculation yields a non-physical velocity result that exceeds the speed of light, indicating that such a wavelength for an electron is not realistic in classical physics.

Step-by-step explanation:

To calculate how fast an electron is moving given its wavelength, we apply the de Broglie equation which relates an electron's wavelength λ to its velocity v according to the formula λ = h/(m*v), where h is the Planck constant (6.626 x 10^-34 m^2 kg/s), m is the mass of the electron (9.109 x 10^-31 kg), and v is the velocity of the electron. Rearranging the formula for v, we get v = h/(m*λ).

Let's compute the velocity of an electron with a wavelength of 5.00 x 10^27 m:

v = (6.626 x 10^-34 m^2 kg/s) / ((9.109 x 10^-31 kg) * (5.00 x 10^27 m))

v = (6.626 x 10^-34) / (4.5545 x 10^-3)

v = 1.4542 x 10^31 m/s

However, this result is not physically possible because it significantly exceeds the speed of light, which is the maximum speed limit in the universe (approximately 3 x 10^8 m/s). Therefore, the given wavelength for the electron is not physically realistic, and such a scenario would be considered non-physical in the framework of classical physics.

User Matt Hulse
by
8.7k points