Answer:
λ = [tex]1.06 * 10^{-11} m[/tex]
Explanation:
Using the De Broglie equation, the characteristic wavelength is given by:
λ = [tex]\frac{h}{p}[/tex]
where
h = Planck's constant = [tex]6.626 * 10^{-34}[/tex] Js.
p = momentum
Momentum, p, can be calculated using:
p = [tex]\sqrt{2Em}[/tex]
where
m = mass of the electron = [tex]9.11 * 10^{-31}[/tex] kg
E = Energy of the electron = 13.4 keV = [tex]13.4 * 10^3 * 1.6 * 10^{-19}[/tex] J = [tex]2.144 * 10^{-15}[/tex] J
=> p = [tex]\sqrt{2 * 2.144 * 10^{-15} * 9.11 * 10^{-31}}[/tex]
p = [tex]\sqrt{3.906 * 10^{-45}}[/tex]
p = [tex]6.250 * 10^{-23}[/tex] kgm/s
Therefore, characteristic wavelength, λ, is:
λ = [tex]\frac{6.626 * 10^{-34}}{6.250 * 10^{-23}}[/tex]
λ = [tex]1.06 * 10^{-11} m[/tex]
