362,417 views
2 votes
2 votes
Calculate the velocity of a non-relativistic electron whose de broglie wavelength is 3.637 nm.

User Derk Jan Speelman
by
2.7k points

2 Answers

19 votes
19 votes

Answer: 2 x 10^5 m/s

Step-by-step explanation:

de Broglie wavelength equation: λ = h / mv

v = h / m · λ

m = 9.11 x 10^-31 kg

h = 6.62 x 10^-34 J·s

λ = 3.637 x 10^-9 m

v = (6.62 x 10^-34 J·s) / (9.11 x 10^-31 kg) (3.637 x 10^-9 m)

v = 199800.3807 = 2 x 10^5 m/s

User Jay Stramel
by
2.5k points
27 votes
27 votes

Answer:

The velocity of a non-relativistic electron can be calculated using the formula v = h / mλ, where h is Planck's constant, m is the mass of the electron, and λ is the de Broglie wavelength of the electron.

Assuming the mass of the electron is 9.11 x 10^-31 kg, the velocity of the electron can be calculated as follows:

v = (6.63 x 10^-34 m^2 kg / s) / (9.11 x 10^-31 kg * 3.637 x 10^-9 m)

This works out to be approximately 5.82 x 10^6 m/s.

However, it's important to note that the de Broglie wavelength of a particle is generally only considered to be a meaningful quantity when the particle is moving at speeds that are comparable to the speed of light. For non-relativistic particles, such as an electron moving at a low velocity, the de Broglie wavelength is not a well-defined concept. Therefore, it's not meaningful to calculate the velocity of an electron based on its de Broglie wavelength.

Step-by-step explanation:

User Tyren
by
2.4k points