The particle and wave nature of matter are demonstrated in the equation

Answer Details

The equation that demonstrates the particle and wave nature of matter is the second option: λ = h/P. This equation is known as the de Broglie wavelength equation, and it relates the wavelength of a particle to its momentum. This equation implies that particles, like waves, can have a wavelength and frequency, which is a property of waves. In other words, it shows that particles have a dual nature, they can behave as both particles and waves.
The first option, λ = hc/E, is the equation for the energy of a photon, which demonstrates the wave nature of light. The third option, λ = c/f, is the equation for the wavelength of light, which also demonstrates the wave nature of light. The fourth option, λ = 2dsinθ, is the equation for the diffraction of waves, which is also a property of waves.