Just as light waves have particle behavior, a moving particle has a wave nature.

Question

Just as light waves have particle behavior, a moving particle has a wave nature. The faster the particle is moving, the higher its kinetic energy and the shorter its wavelength. The wavelength, , of a particle of mass m, and moving at velocity v, is given by the de Broglie relation

=hmv

where h=6.626×1034 Js is Planck's constant.

This formula applies to all objects, regardless of size, but the de Broglie wavelength of macro objects is miniscule compared to their size, so we cannot observe their wave properties. In contrast, the wave properties of subatomic particles can be seen in such experiments as diffraction of electrons by a metal crystal.

The mass of a golf ball is 45.9 g . If it leaves the tee with a speed of 80.0 m/s , what is its corresponding wavelength?

Express your answer with the appropriate units.

Explanation / Answer

so, we have:
v = 80.0 m/s

mass, m = 45.9 g
= 4.59*10^-2 kg

use:
lambda = h / (m*v)
lambda = (6.626*10^-34) / (4.59*10^-2*80)
lambda = 1.804*10^-34 m
Answer: 1.80*10^-34 m

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