Question #e7625

1 Answer
Jose
Feb 7, 2018

#color(blue)"λ "prop"##(1/sqrtV)"#

Explanation:

#color(blue)"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.

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