Question

Question #d42ce

Answer 1

de Broglie suggested that particles can behave like waves.

de Broglie postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as wave-particle duality.

Every particle of matter with mass m and velocity v has a momentum `p = mv`. de Broglie assumed that any particle had a wavelength `λ` that was equal to Planck's constant `h` divided by its momentum.

`λ = h/p = h/(mv)`

EXAMPLE

What is the de Broglie wavelength of an electron (#"mass" = 9.11 xx 10^-31"kg"#) moving at a speed of `6.00 xx 10^6"m/s"`?

Solution

`λ = h/(mv) = (6.626 × 10^-34 cancel("kg")·"m"^cancel("2")cancel("s⁻¹"))/( 9.11 × 10^-31 cancel("kg") × 6.00 × 10^6 cancel("m·s⁻¹"))`
`= 1.21×10^-10"m"`

Note: This is just a little bigger than the diameter of a hydrogen atom.