Help...Modern Physics; The Wavelike property of Particles?

Question

How slow would an electron have to be traveling for its wavelength to be at least 1 micro meter???

Answer 1

The DeBroglie wavelength is:
lambda = h / p

For a slow (non-relativistic) electron, momentum is given by:
p = mv

so wavelength = h / mv
Solve for the speed:
v = h / (m lambda)
They give you the wavelength. Look up the mass of the electron. Look up planck's constant (h). Plugnchug.

Answer 2

If The electron is moving has a free particle it would move at a constant mass.

If the electron is moving relative to the nucleus of the Atom it would move at a variable mass.So the Wavelenght of the electron would vary as a function of its relativistic mass.
And as per Heisenberg's Principle of uncertainty it is impossible to measure momentum and mass at the same time.

If the Electrom moves as a free particle outside the influence of the Nucleus of an atom. The Electron's motion would also be oscialliatory. However its wave lenght is many fold smaller than one micrometer.The actual wavelenght of one free electron on earth is aprox 2.85 Femtos, moving at a frequency of aprox.1.45 x10^20 Herz.

Whereas one micromass of light corpuscule moves at a frequency of aprox.7.4 x10^42 herz.

Answer 3

the wavelength =h/mv
h: plank constant = 6.625 x 10^(-34) Js
p: momentum
m: mass of electron
(assum that v << c)
1 um = 10^(-6) m
v = 6.625 x 10^(-34)/[10^(-6) x 9.1 ^(-31)]
v = 0. 73 x 10^3 m/s << c

Answer 4

18 miles per hour