The formula to determine the wavelength is, De-Broglie wavelength formula:
[tex]\lambda =\frac{h}{mv}[/tex] -(1)
where, [tex]\lambda[/tex] is wavelength, m is mass, v is velocity and h is Planck's constant = [tex]6.63\times 10^{-34} Js[/tex] = [tex]6.63\times 10^{-34} kgm^{2}s^{-1}[/tex]
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, [tex]1 mph = \frac{1.609\times 10^{3} ms^{-1}}{60\times 60}[/tex]
So, [tex]90 mph = \frac{91\times 1.609\times 10^{3} ms^{-1}}{60\times 60}[/tex] = [tex]40.67 ms^{-1}[/tex]
Substituting the values in formula 1:
[tex]\lambda =\frac{6.63\times 10^{-34} kgm^{2}s^{-1}}{0.147 kg\times 40.67 ms^{-1}}[/tex]
[tex]\lambda =1.11\times 10^{-34} m[/tex]
Hence, the wavelength wavelength of a 147-g baseball traveling at 91.0 mph is
[tex]1.11\times 10^{-34} m[/tex].
