What is the de Broglie wavelength of a ball with a mass of 0.20 kg when it strikes the ground after it has been dropped from a building that's 50 m tall?

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Answer 1 · 2014-07-16T13:17:39

The de Broglie wavelength of the ball is 1.06 × 10⁻³⁴ m.

The de Broglie equation is

# λ = h/(mv)#

We know #h# and #m#. So we must calculate #v#.

For this, we need to know the physics formula for the velocity of a falling object after it has dropped a given distance:

#v = √(2gy)#, where #g# is the acceleration due to gravity and #y# is the distance fallen.

#v =√(2 × 9.806 m·s⁻² × 50 m) = √(9806 m²s⁻²)# = 31.31 m·s⁻¹ (2 significant figures + 2 guard digits)

# λ = h/(mv) = (6.626 × 10⁻³⁴ kg·m²s⁻¹)/(0.20 kg × 31.31 m·s⁻¹)# =1.06 × 10⁻³⁴ m