2 Answers

Ezequiel Ramiro · Answer 1 · 2019-10-13T22:37:21+0000

The formula to determine the wavelength is, De-Broglie wavelength formula:

$\lambda =(h)/(mv)$ -(1)

where,
$\lambda$ is wavelength, m is mass, v is velocity and h is Planck's constant =
6.63* 10^(-34) Js =
6.63* 10^(-34) kgm^(2)s^(-1)

mass, m = 147 g (given)

Since, 1 g = 0.001 kg

So, 147 g = 0.147 kg

v = 91.0 mph (given)

Converting mph to mps:

Since,
1 mph = (1.609* 10^(3) ms^(-1))/(60* 60)

So,
90 mph = (91* 1.609* 10^(3) ms^(-1))/(60* 60) =
40.67 ms^(-1)

Substituting the values in formula 1:

$\lambda =(6.63* 10^(-34) kgm^(2)s^(-1))/(0.147 kg* 40.67 ms^(-1))$

$\lambda =1.11* 10^(-34) m$

Hence, the wavelength wavelength of a 147-g baseball traveling at 91.0 mph is

1.11* 10^(-34) m .

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