Question

Compare and contrast properties of waves and particles, explaining which properties can and cannot distinguish between wave-like behaviour and particle-like behaviour.

Answer 1

Properties of waves: wavelength $\lambda$, frequency f and velocity v. Properties of particles: mass m, charge q, and other quantum numbers. Mass and wavelength, according to De Broglie wavelength equation, can help to distinguish what it is - a wave or a particle:

$$\lambda=\frac{h}{mv}.$$

The shorter the wavelength, the more the object behaves like a particle. On the other hand, this can be also said in terms of frequency:

$$\lambda=\frac{v}{f}=\frac{h}{mv},\\ \space\\ f=\frac{mv^2}{h}.$$

Higher frequencies define particle-like behavior.

Waves can diffract and interfere, while particles cannot. We can say that it is possible to apply Newton's mechanics and kinematics to particles, but not to waves.