Answer:
V = 6.04 10⁻⁶ V
Explanation:
The energy in a system is conserved so the potential energy of the system must be transformed into the kinetic energy of the electron.
[tex]E_{p}[/tex] = K
eV = ½ m v²
V = ½ m v²/e
Let's use the de Broglie relation
λ= h / p
the moment is
p = mv
let's replace
λ = h / mv
v = [tex]\frac{h}{m \lambda }[/tex]
hence the potential energy
V = ½ [tex]\frac{m}{e}[/tex] (\frac{h}{m \lambda })²
[tex]V = \frac{h^{2} }{2e m \lambda^{2} }[/tex]
let's reduce λ to sistem SI
λ = 500 nm = 500 10⁻⁹ m = 5 10⁻⁷ m
let's calculate
V = (6.63 10⁻³⁴)² / (9.1 10⁻³¹ 1.6 10⁻¹⁹ (5 10⁻⁷)² )
V = 6.04 10⁻⁶ V
