Question

Calculate the wavelength of a softball with a mass of 100 g traveling at a velocity of 35 m s^–1, assuming that it can be modeled as a single particle.

Short answer

The wavelength of the softball is \({\rm{1}}{\rm{.89 \times 1}}{{\rm{0}}^{{\rm{ - 34}}}}{\rm{m}}\)

Step-by-step solution

analyzing the given data  

Given; Mass of the softball = 100 g

Velocity = 35 m/s

To find; the wavelength of the softball

determining the wavelength of the softball  

\(\begin{aligned}{\rm{\lambda = }}\frac{{\rm{h}}}{{{\rm{m}}\nu }}\\{\rm{\lambda = }}\frac{{{\rm{6}}{\rm{.626 \times 1}}{{\rm{0}}^{{\rm{ - 34}}}}{\rm{m}}{{\rm{s}}^{{\rm{ - 1}}}}}}{{{\rm{100 \times 1}}{{\rm{0}}^{{\rm{ - 4}}}}{\rm{ \times 35}}}}\\{\rm{\lambda = 1}}{\rm{.89 \times 1}}{{\rm{0}}^{{\rm{ - 34}}}}{\rm{m}}\end{aligned}\)

Hence, the wavelength of the softball is \({\rm{\lambda = 1}}{\rm{.89 \times 1}}{{\rm{0}}^{{\rm{ - 34}}}}{\rm{m}}\)