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 69 mph.

Answer 1

The de Broglie wavelength associated with a baseball is
`9.763* 10^(-26) nm`.

Step-by-step explanation:

De-Broglie wavelength is calculated by using the formula:

`\lambda=(h)/(mv)` .....(1)

where,

`\lambda` = wavelength of particle

h = Planck's constant =
`6.626* 10^(-34)Js`

m = mass of particle

v = velocity of particle

We have :

m = 220 g =0.220 kg

velocity of the baseball , v= 69 mile/h

1 mile = 1609.34 m , 1 hour = 3600 s

v =
`(69* 1609.34 m)/(3600 s)=30.85 m/s`

`\lambda=(6.626* 10^(-34)Js)/(0.220 kg* 30.85 m/s)`

`\lambda =9.763* 10^(-35) m= 9.763* 10^(-26) nm`

(
`1 m = 10^9 nm`)

The de Broglie wavelength associated with a baseball is
`9.763* 10^(-26) nm`.