De Broglie Wavelength

Question 2.

In order to derive the equation, λ = h/(√(2mKE)), we must use the equations for kinetic energy, KE = ½ m*v², and linear momentum, p = m*v.

If we solve the KE equation for v:

KE = ½ m*v²

(2*KE)/m = v²

√ ((2*KE)/m) = v

Then substitute in v for the v in the linear momentum equation:

p = m*v

p = m* √ ((2*KE)/m)

Use the equation from question 1 and substitute in the equation for linear momentum that contains the KE equation:

λ = h / p

λ = h / (m* √ ((2*KE)/m))

Now square both sides of the equation:

λ² = h² / (m²* (2*KE)/m)

The two m’s on the bottom cancel and you are left with:

λ² = h² / (m*2*KE)

Finally take the square root of both sides:

λ = h / √ (2*m*KE)