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

`1.604* 10^(-25) nm` is the de Broglie wavelength associated with a baseball that is moving with a velocity of 42 mph.

Step-by-step explanation:

De-Broglie's wavelength, which is:

`\lambda=(h)/(mv)`

where,

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

h = Planck's constant =
`6.626* 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 =
`(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 =(6.626* 10^(-34)Js)/(0.220 kg* 18.78 m/s)</p><p>`=1.604\times 10^{-34} m=1.604\times 10^{-25} nm[/tex]

`1 m = 10^9 nm`

`1.604* 10^(-25) nm` is the de Broglie wavelength associated with a baseball that is moving with a velocity of 42 mph.