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

Answer:

$2.54\cdot 10^{-34}m$

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,

$v=\sqrt{2gh}=\sqrt{2(9.8 m/s^2)(39.8 m)}=27.9 m/s$

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:

$\lambda = \frac{h}{p}=\frac{6.63\cdot 10^{-34} Js}{2.61 kg m/s}=2.54\cdot 10^{-34}m$