28.0k views
2 votes
What is the de Broglie wavelength of an electron (M=9.11×10^-31 kgmoving at a velocity of 10 of the speed of light?

a. 5.5×10^−11m
b. 2.2×10^-11 m

c. 1.1×10 ^−11m
d. 8.7×10 ^−12m

1 Answer

6 votes

Final answer:

The de Broglie wavelength of an electron moving at 10% of the speed of light is calculated to be 2.42×10-12 m, which does not match any of the options provided in the question.

Step-by-step explanation:

The de Broglie wavelength (λ) of a particle is given by the formula λ = h / p, where h is Planck's constant (6.626×10-34 m2kg/s) and p is the momentum of the particle. For an electron with a mass (M) of 9.11×10-31 kg moving at 10% of the speed of light (c), its momentum (p) would be its mass times its velocity (v), i.e. p = M × v. Given that the speed of light c is approximately 3.00×108 m/s, 10% of this speed is 3.00×107 m/s. Inserting the values, we get λ = (6.626×10-34 m2kg/s) / (9.11×10-31 kg × 3.00×107 m/s), which calculates to λ = 2.42×10-12 m. Therefore, none of the provided options (a, b, c, or d) are correct.

User Neil Moss
by
7.0k points