Question

A baseball weighs 220 g. Top speed for a professional pitcher is about 100 mph when he throws a fast ball. Find the de Broglie wavelength (in nm) associated with a baseball that is moving with a velocity of 42 mph

Answer 1

Answer:

$1.604\times 10^{-25} nm$ is the de Broglie wavelength associated with a baseball that is moving with a velocity of 42 mph.

Explanation:

De-Broglie's wavelength, which is:

$\lambda=\frac{h}{mv}$

where,

$\lambda$ = De-Broglie's wavelength = ?

h = Planck's constant = $6.626\times 10^{-34}Js$

m = mass of particle  =

v = velocity of the particle

We have :

Mass of baseball = m = 220 g = 0.220 kg ( 1g = 0.001 kg)

Velocity of the base ball = v = 42mph =$\frac{42}{2.237} m/s=18.78 m/s$

1 m/s = 2.237 mph

De-Broglie wavelength of the baseball at v:$\lambda$

$\lambda =\frac{6.626\times 10^{-34}Js}{0.220 kg\times 18.78 m/s}$=1.604\times 10^{-34} m=1.604\times 10^{-25} nm[/tex]

$1 m = 10^9 nm$

$1.604\times 10^{-25} nm$ is the de Broglie wavelength associated with a baseball that is moving with a velocity of 42 mph.