The mass of an electron is 9.11×10−31 kg. if the de broglie wavelength for an electron in a hydrogen atom is 3.31×10−10 m, how fast is the electron moving relative to the speed of light? the speed of light is 3.00×108 m/s.

The electron moves slower than the speed of light

Explanation:

The de Broglie wavelength is given by the following formula:

(1)

Where:

is the Planck constant

is the momentum of the atom, which is given by:

(2)

Where:

is the mass of the electron

is the velocity of the electron  (the value we want to find)

Substituting (2) in (1):

(3)

Finding :

(4)

(5)

Finally:

>>> This is the velocity of the electron, which compared to the of the light is quite slower.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

0 = 0.40 / 0 = 0

= 0.20 = 9.80 ⁄2 =?

=0 , = = 0.20 =0.50 0 0.40 ⁄

=0−122 =0−12(9.80 ⁄2)(0.50)2 =1.2