Question

What is its characteristic wavelength? [Hint: Recall that the kinetic energy of a moving object is E=12mv2, where m is the mass of the object and v is the speed of the object.]

Answer 1

Answer:

λ =  $1.06 * 10^{-11} m$

Explanation:

Using the De Broglie equation, the characteristic wavelength is given by:

λ = $\frac{h}{p}$

where

h = Planck's constant = $6.626 * 10^{-34}$ Js.

p = momentum

Momentum, p, can be calculated using:

p =  $\sqrt{2Em}$

where

m = mass of the electron = $9.11 * 10^{-31}$ kg

E = Energy of the electron = 13.4 keV = $13.4 * 10^3 * 1.6 * 10^{-19}$ J = $2.144 * 10^{-15}$ J

=> p = $\sqrt{2 * 2.144 * 10^{-15} * 9.11 * 10^{-31}}$

p = $\sqrt{3.906 * 10^{-45}}$

p = $6.250 * 10^{-23}$ kgm/s

Therefore, characteristic wavelength, λ, is:

λ =  $\frac{6.626 * 10^{-34}}{6.250 * 10^{-23}}$

λ =  $1.06 * 10^{-11} m$