diff --git a/docs/sph4u7.md b/docs/sph4u7.md index ca19bcf..3dad967 100644 --- a/docs/sph4u7.md +++ b/docs/sph4u7.md @@ -518,6 +518,20 @@ $$hf_i+\frac{1}{2}mv^2_{ei}=hf_f + \frac{1}{2}mv^2_{ef}$$ In general, the momentum of a photon is equal to, where $h$ is Planck's constant and $\lambda$ is the wavelength of the light: $$p=\frac{h}{\lambda}$$ +## Matter waves + +Particles/waves cannot act like particles and waves at the same time. For a given observation, it adopts the property of one or the other. In reality, all particles exhibit wave properties *sometimes* and all waves exhibit particle properties *sometimes*. + +By equating the equations for momentum of photons and particles, the wavelength of a particle can be determined. Where $\lambda$ is the wavelength of the particle, $m$ is its mass, $v$ is its velocity, and $h$ is Planck's constant: +$$\lambda=\frac{h}{mv}$$ + +Therefore, wavelengths of "particles" are only really significant for small masses at high speeds rather than large masses at lower speeds. + +!!! example + A 50 kg mass moving at 16 m/s is has a wavelength many orders of magnitude smaller than a quark and will not display any observable wave behaviours. + +The discovery of wave-particle duality has led to advancements in technology such as the scanning electron microscope. + ## Resources - [IB Physics Data Booklet](/resources/g11/ib-physics-data-booklet.pdf)