Question

A ball has a mass of 0.0935 kg just before it strikes the Earth after being dropped from a building 39.8 m tall. What is its de Broglie wavelength? The acceleration of gravity is 9.8 m/s 2 and Planck’s constant is 6.62607 × 10−34 J · s. Answer in units of m.

Answer 1

`2.54\cdot 10^(-34)m`

Step-by-step explanation:

First of all, we need to find the final velocity of the ball just before it reaches the ground. Since the ball is in free-fall motion, its final velocity is given by

`v^2 = u^2 +2gh`

where

v is the final velocity

u = 0 is the initial velocity

g = 9.8 m/s^2 is the acceleration due to gravity

h = 39.8 m is the height of the building

Solving for v,

`v=√(2gh)=√(2(9.8 m/s^2)(39.8 m))=27.9 m/s`

Now we can calculate the ball's momentum:

`p=mv=(0.0935 kg)(27.9 m/s)=2.61 kg m/s`

And now we can calculate the De Broglie's wavelength of the ball:

`\lambda = (h)/(p)=(6.63\cdot 10^(-34) Js)/(2.61 kg m/s)=2.54\cdot 10^(-34)m`