Question #e7625

1 Answer
Feb 7, 2018

color(blue)"λ "prop"λ (1/sqrtV)"(1V)

Explanation:

color(blue)"De Broglie Wavelength Formula"De Broglie Wavelength Formula

Light can travel like a wave or like a particle (photons). Louis de Broglie (1892-1987) related both light movements. The formula relates the wavelength to the momentum of a wave/particle.

λ = h/p

Re-arrenging

p = m nu = h/λ

λ = the de Broglie wavelength (m)
h = Planck's constant ()
p = momentum of a particle ()
m = mass of a particle (kg)
nu = velocity of a particle (m/s)

Making squares both members of equation

m^2 nu^2 = h^2/λ^2"

Dividing both sides by 2m

"(m^2 nu^2 )"/"2m"= "("h^2""λ^2")/"2m"

1/2"m nu^2 "= "("h^2"/"2m)"""(1/λ^2)"

But since the kinetic energy of the electron is equal to the energy gained from accelerating through the electric potential,

eV "= "("h^2"/"2m)"""(1/λ^2)"

Re-arrenging

λ^2 = h^2/"2 m e V"

λ = h/"2 m e "(1/sqrtV)

Finally,

color(blue)"λ "prop"(1/sqrtV)"

Personal opinion: similar to "thermocouple" (Seebeck) effect.